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797 relations: Absorbing set (random dynamical systems), Actuarial notation, Actuarial present value, Actuarial reserves, Adapted process, Addition, Additive Markov chain, Aleatoricism, Algebra of random variables, Algebraic formula for the variance, Algebraic statistics, Algorithmic cooling, Algorithmic inference, Algorithmic Lovász local lemma, An Essay towards solving a Problem in the Doctrine of Chances, Analysis of variance, Anderson's theorem, Anscombe transform, Anton Formann, Arbitrarily varying channel, Areas of mathematics, Artificial neural network, Asymmetric Laplace distribution, Asymptotic distribution, Asymptotic theory (statistics), Autocorrelation, Autoregressive model, Łukaszyk–Karmowski metric, Bank condition, Bapat–Beg theorem, Basu's theorem, Bayes factor, Bayes' theorem, Bayesian game, Bayesian hierarchical modeling, Bayesian multivariate linear regression, Bayesian network, Bayesian probability, Bayesian programming, Bayesian vector autoregression, Bayesian-optimal mechanism, Bayesian-optimal pricing, Behrens–Fisher distribution, Belief propagation, Benford's law, Bernoulli distribution, Bernoulli process, Bernoulli scheme, Bernoulli trial, Bernstein polynomial, ..., Besov measure, Beta distribution, Beta function, Beta negative binomial distribution, Beta-binomial distribution, Bialgebra, Bienaymé's identity, Big O in probability notation, Binary data, Binary entropy function, Binary erasure channel, Binary symmetric channel, Binomial distribution, Binomial process, Binomial regression, Binomial sum variance inequality, Binomial type, Birnbaum–Orlicz space, Blackboard bold, Boltzmann machine, Bootstrapping populations, Borel distribution, Borel–Cantelli lemma, Box–Cox distribution, Box–Jenkins method, Branching process, Branching random walk, Brownian web, Bruno de Finetti, Buffon's needle, Burr distribution, Canonical correlation, Cantelli's inequality, Cantor distribution, Carl-Gustav Esseen, Catalog of articles in probability theory, Categorical distribution, Categorical variable, Cauchy distribution, Cauchy–Schwarz inequality, Causal inference, Central limit theorem, Central limit theorem for directional statistics, Central moment, Chain rule (probability), Champernowne distribution, Characteristic function (probability theory), Characterization of probability distributions, Charles M. 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Absorbing set (random dynamical systems)

In mathematics, an absorbing set for a random dynamical system is a subset of the phase space that eventually contains the image of any bounded set under the cocycle ("flow") of the random dynamical system.

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Actuarial notation

Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables.

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Actuarial present value

The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made).

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Actuarial reserves

An actuarial reserve is a liability equal to the actuarial present value of the future cash flows of a contingent event.

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Adapted process

In the study of stochastic processes, an adapted process (also referred to as a non-anticipating or non-anticipative process) is one that cannot "see into the future".

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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Additive Markov chain

In probability theory, an additive Markov chain is a Markov chain with an additive conditional probability function.

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Aleatoricism

Aleatoricism is the incorporation of chance into the process of creation, especially the creation of art or media.

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Algebra of random variables

The algebra of random variables provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory.

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Algebraic formula for the variance

In probability theory and statistics, there are several algebraic formulae for the variance available for deriving the variance of a random variable.

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Algebraic statistics

Algebraic statistics is the use of algebra to advance statistics.

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Algorithmic cooling

Algorithmic cooling is an algorithmic method for transferring heat (or entropy) from some qubits to others or outside the system and into the environment, which results in a cooling effect.

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Algorithmic inference

Algorithmic inference gathers new developments in the statistical inference methods made feasible by the powerful computing devices widely available to any data analyst.

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Algorithmic Lovász local lemma

In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence.

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An Essay towards solving a Problem in the Doctrine of Chances

An Essay towards solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by the Reverend Thomas Bayes, published in 1763, two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price.

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Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

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Anderson's theorem

In mathematics, Anderson's theorem is a result in real analysis and geometry which says that the integral of an integrable, symmetric, unimodal, non-negative function f over an n-dimensional convex body K does not decrease if K is translated inwards towards the origin.

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Anscombe transform

In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution.

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Anton Formann

Anton K. Formann (August 27, 1949, Vienna, Austria – July 12, 2010, Vienna) was an Austrian research psychologist, statistician, and psychometrician.

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Arbitrarily varying channel

An arbitrarily varying channel (AVC) is a communication channel model used in coding theory, and was first introduced by Blackwell, Breiman, and Thomasian.

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Areas of mathematics

Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics.

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Artificial neural network

Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.

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Asymmetric Laplace distribution

In probability theory and statistics, the asymmetric Laplace distribution (ALD) is a continuous probability distribution which is a generalization of the Laplace distribution.

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Asymptotic distribution

In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions.

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Asymptotic theory (statistics)

In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests.

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Autocorrelation

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.

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Autoregressive model

In statistics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc.

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Łukaszyk–Karmowski metric

In mathematics, the Łukaszyk–Karmowski metric is a function defining a distance between two random variables or two random vectors.

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Bank condition

Bank condition is a random variable used to represent the probability of failure of a bank.

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Bapat–Beg theorem

In probability theory, the Bapat–Beg theorem gives the joint probability distribution of order statistics of independent but not necessarily identically distributed random variables in terms of the cumulative distribution functions of the random variables.

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Basu's theorem

In statistics, Basu's theorem states that any boundedly complete sufficient statistic is independent of any ancillary statistic.

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Bayes factor

In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing.

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Bayes' theorem

In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes' rule, also written as Bayes’s theorem) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

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Bayesian game

In game theory, a Bayesian game is a game in which the players have incomplete information on the other players (e.g. on their available strategies or payoffs), but, they have beliefs with known probability distribution.

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Bayesian hierarchical modeling

Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.

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Bayesian multivariate linear regression

In statistics, Bayesian multivariate linear regression is a Bayesian approach to multivariate linear regression, i.e. linear regression where the predicted outcome is a vector of correlated random variables rather than a single scalar random variable.

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Bayesian network

A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG).

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Bayesian probability

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.

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Bayesian programming

Bayesian programming is a formalism and a methodology to specify probabilistic models and solve problems when less than the necessary information is available.

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Bayesian vector autoregression

In statistics, Bayesian vector autoregression (BVAR) uses Bayesian methods to estimate a vector autoregression (VAR).

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Bayesian-optimal mechanism

A Bayesian-optimal mechanism (BOM) is a mechanism in which the designer does not know the valuations of the agents for whom the mechanism is designed, but he knows that they are random variables and he knows the probability distribution of these variables.

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Bayesian-optimal pricing

Bayesian-optimal pricing (BO pricing) is a kind of algorithmic pricing in which a seller determines the sell-prices based on probabilistic assumptions on the valuations of the buyers.

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Behrens–Fisher distribution

In statistics, the Behrens–Fisher distribution, named after Ronald Fisher and Walter Behrens, is a parameterized family of probability distributions arising from the solution of the Behrens–Fisher problem proposed first by Behrens and several years later by Fisher.

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Belief propagation

Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

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Benford's law

Benford's law, also called Newcomb-Benford's law, law of anomalous numbers, and first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data.

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Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q.

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Bernoulli process

In probability and statistics, a Bernoulli process is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1.

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Bernoulli scheme

In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes.

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Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

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Bernstein polynomial

In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of Bernstein basis polynomials.

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Besov measure

In mathematics — specifically, in the fields of probability theory and inverse problems — Besov measures and associated Besov-distributed random variables are generalisations of the notions of Gaussian measures and random variables, Laplace distributions, and other classical distributions.

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Beta distribution

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.

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Beta function

In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for.

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Beta negative binomial distribution

In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X equal to the number of failures needed to get r successes in a sequence of independent Bernoulli trials where the probability p of success on each trial is constant within any given experiment but is itself a random variable following a beta distribution, varying between different experiments.

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Beta-binomial distribution

In probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers arising when the probability of success in each of a fixed or known number of Bernoulli trials is either unknown or random.

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Bialgebra

In mathematics, a bialgebra over a field K is a vector space over K which is both a unital associative algebra and a coalgebra.

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Bienaymé's identity

In probability theory, Bienaymé's identity states that where X_1, \ldots, X_n are pairwise independent integrable random variables with finite second moments and S_n.

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Big O in probability notation

The order in probability notation is used in probability theory and statistical theory in direct parallel to the big-O notation that is standard in mathematics.

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Binary data

Binary data is data whose unit can take on only two possible states, traditionally termed 0 and +1 in accordance with the binary numeral system and Boolean algebra.

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Binary entropy function

In information theory, the binary entropy function, denoted \operatorname H(p) or \operatorname H_\text(p), is defined as the entropy of a Bernoulli process with probability p of one of two values.

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Binary erasure channel

disambiguation: Landauer's principle A binary erasure channel (or BEC) is a common communications channel model used in coding theory and information theory.

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Binary symmetric channel

A binary symmetric channel (or BSC) is a common communications channel model used in coding theory and information theory.

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Binomial distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.

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Binomial process

A binomial process is a special point process in probability theory.

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Binomial regression

In statistics, binomial regression is a technique in which the response (often referred to as Y) is the result of a series of Bernoulli trials, or a series of one of two possible disjoint outcomes (traditionally denoted "success" or 1, and "failure" or 0).

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Binomial sum variance inequality

The binomial sum variance inequality states that the variance of the sum of binomially distributed random variables will always be less than or equal to the variance of a binomial variable with the same ''n'' and ''p'' parameters.

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Binomial type

In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities Many such sequences exist.

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Birnbaum–Orlicz space

In the mathematical analysis, and especially in real and harmonic analysis, a Birnbaum–Orlicz space is a type of function space which generalizes the L''p'' spaces.

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Blackboard bold

Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled.

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Boltzmann machine

A Boltzmann machine (also called stochastic Hopfield network with hidden units) is a type of stochastic recurrent neural network (and Markov random field).

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Bootstrapping populations

Starting with a sample \ observed from a random variable X having a given distribution law with a set of non fixed parameters which we denote with a vector \boldsymbol\theta, a parametric inference problem consists of computing suitable values – call them estimates – of these parameters precisely on the basis of the sample.

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Borel distribution

The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory.

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Borel–Cantelli lemma

In probability theory, the Borel–Cantelli lemma is a theorem about sequences of events.

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Box–Cox distribution

In statistics, the Box–Cox distribution (also known as the power-normal distribution) is the distribution of a random variable X for which the Box–Cox transformation on X follows a truncated normal distribution.

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Box–Jenkins method

In time series analysis, the Box–Jenkins method, named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series.

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Branching process

In probability theory, a branching process is a type of mathematical object known as a stochastic process, which consists of collections of random variables.

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Branching random walk

In probability theory, a branching random walk is a stochastic process that generalizes both the concept of a random walk and of a branching process.

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Brownian web

In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time.

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Bruno de Finetti

Bruno de Finetti (13 June 1906 – 20 July 1985) was an Italian probabilist statistician and actuary, noted for the "operational subjective" conception of probability.

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Buffon's needle

In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: Buffon's needle was the earliest problem in geometric probability to be solved; it can be solved using integral geometry.

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Burr distribution

In probability theory, statistics and econometrics, the Burr Type XII distribution or simply the Burr distribution is a continuous probability distribution for a non-negative random variable.

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Canonical correlation

In statistics, canonical-correlation analysis (CCA) is a way of inferring information from cross-covariance matrices.

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Cantelli's inequality

In probability theory, Cantelli's inequality, named after Francesco Paolo Cantelli, is a generalization of Chebyshev's inequality in the case of a single "tail".

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Cantor distribution

The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.

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Carl-Gustav Esseen

Carl-Gustav Esseen (18 September 1918, Linköping – 10 November 2001) was a Swedish mathematician.

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Catalog of articles in probability theory

This page lists articles related to probability theory.

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Categorical distribution

In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified.

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Categorical variable

In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

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Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

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Cauchy–Schwarz inequality

In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.

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Causal inference

Causal inference is the process of drawing a conclusion about a causal connection based on the conditions of the occurrence of an effect.

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Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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Central limit theorem for directional statistics

In probability theory, the central limit theorem states conditions under which the average of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.

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Central moment

In probability theory and statistics, a central moment is a moment of a probability distribution of a random variable about the random variable's mean; that is, it is the expected value of a specified integer power of the deviation of the random variable from the mean.

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Chain rule (probability)

In probability theory, the chain rule (also called the general product rule) permits the calculation of any member of the joint distribution of a set of random variables using only conditional probabilities.

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Champernowne distribution

In statistics, the Champernowne distribution is a symmetric, continuous probability distribution, describing random variables that take both positive and negative values.

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Characteristic function (probability theory)

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.

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Characterization of probability distributions

In mathematics in general, a characterization theorem says that a particular object – a function, a space, etc.

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Charles M. Stein

Charles M. Stein (March 22, 1920 – November 24, 2016) was an American mathematical statistician and professor of statistics at Stanford University.

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Chebyshev's inequality

In probability theory, Chebyshev's inequality (also spelled as Tchebysheff's inequality, Нера́венство Чебышёва, also called Bienaymé-Chebyshev inequality) guarantees that, for a wide class of probability distributions, no more than a certain fraction of values can be more than a certain distance from the mean.

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Chernoff's distribution

In probability theory, Chernoff's distribution, named after Herman Chernoff, is the probability distribution of the random variable where W is a "two-sided" Wiener process (or two-sided "Brownian motion") satisfying W(0).

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Chi-squared distribution

No description.

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Christoph Schönborn

Christoph Maria Michael Hugo Damian Peter Adalbert, Count of Schönborn, O.P. (German: Christoph Maria Michael Hugo Damian Peter Adalbert, Graf von Schönborn; born 22 January 1945), is a Bohemian-born Austrian Dominican friar and theologian, who is a cardinal of the Catholic Church.

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Chvátal–Sankoff constants

In mathematics, the Chvátal–Sankoff constants are mathematical constants that describe the lengths of longest common subsequences of random strings.

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Circular distribution

In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range.

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CLs method (particle physics)

In particle physics, CLs represent a statistical method for setting upper limits (also called exclusion limits) on model parameters, a particular form of interval estimation used for parameters that can take only non-negative values.

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Cluster labeling

In natural language processing and information retrieval, cluster labeling is the problem of picking descriptive, human-readable labels for the clusters produced by a document clustering algorithm; standard clustering algorithms do not typically produce any such labels.

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Cochran's theorem

In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.

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Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications.

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Coherent risk measure

In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have.

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Cokurtosis

In probability theory and statistics, cokurtosis is a measure of how much two random variables change together.

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Combinant

In the mathematical theory of probability, the combinants cn of a random variable X are defined via the combinant-generating function G(t), which is defined from the moment generating function M(z) as which can be expressed directly in terms of a random variable X as wherever this expectation exists.

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Completeness (statistics)

In statistics, completeness is a property of a statistic in relation to a model for a set of observed data.

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Complex random variable

In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers.

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Complex random vector

In probability theory and statistics, a complex random vector is typically a tuple of complex-valued random variables, and generally is a random variable taking values in a vector space over the field of complex numbers.

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Compound Poisson distribution

In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable.

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Compound probability distribution

In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.

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Concentration dimension

In mathematics — specifically, in probability theory — the concentration dimension of a Banach space-valued random variable is a numerical measure of how “spread out” the random variable is compared to the norm on the space.

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Concentration inequality

In probability theory, concentration inequalities provide bounds on how a random variable deviates from some value (typically, its expected value).

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Conditional entropy

In information theory, the conditional entropy (or equivocation) quantifies the amount of information needed to describe the outcome of a random variable Y given that the value of another random variable X is known.

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Conditional expectation

In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value – the value it would take “on average” over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur.

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Conditional independence

In probability theory, two events R and B are conditionally independent given a third event Y precisely if the occurrence of R and the occurrence of B are independent events in their conditional probability distribution given Y. In other words, R and B are conditionally independent given Y if and only if, given knowledge that Y occurs, knowledge of whether R occurs provides no information on the likelihood of B occurring, and knowledge of whether B occurs provides no information on the likelihood of R occurring.

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Conditional probability

In probability theory, conditional probability is a measure of the probability of an event (some particular situation occurring) given that (by assumption, presumption, assertion or evidence) another event has occurred.

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Conditional probability distribution

In probability theory and statistics, given two jointly distributed random variables X and Y, the conditional probability distribution of Y given X is the probability distribution of Y when X is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value x of X as a parameter.

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Conditional probability table

In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables).

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Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling method often applied in pattern recognition and machine learning and used for structured prediction.

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Conditional variance

In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables.

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Conditioning (probability)

Beliefs depend on the available information.

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Confidence interval

In statistics, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown population parameter.

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Conjugate prior

In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same probability distribution family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function.

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Consistency (statistics)

In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely.

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Continuity correction

In probability theory, a continuity correction is an adjustment that is made when a discrete distribution is approximated by a continuous distribution.

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Continuity theorem

In mathematics and statistics, the continuity theorem may refer to one of the following results.

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Continuous stochastic process

In probability theory, a continuous stochastic process is a type of stochastic process that may be said to be "continuous" as a function of its "time" or index parameter.

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Contrast (statistics)

In statistics, particularly in analysis of variance and linear regression, a contrast is a linear combination of variables (parameters or statistics) whose coefficients add up to zero, allowing comparison of different treatments.

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Convergence of measures

In mathematics, more specifically measure theory, there are various notions of the convergence of measures.

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Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables.

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Convex conjugate

In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions.

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

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Convolution of probability distributions

The convolution of probability distributions arises in probability theory and statistics as the operation in terms of probability distributions that corresponds to the addition of independent random variables and, by extension, to forming linear combinations of random variables.

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Convolution power

In mathematics, the convolution power is the n-fold iteration of the convolution with itself.

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Convolution random number generator

In statistics and computer software, a convolution random number generator is a pseudo-random number sampling method that can be used to generate random variates from certain classes of probability distribution.

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Conway–Maxwell–binomial distribution

In probability theory and statistics, the Conway–Maxwell–binomial (CMB) distribution is a three parameter discrete probability distribution that generalises the binomial distribution in an analogous manner to the way that the Conway–Maxwell–Poisson distribution generalises the Poisson distribution.

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Copula (probability theory)

In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform.

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Correction for attenuation

Correction for attenuation is a statistical procedure, due to Spearman (1904), to "rid a correlation coefficient from the weakening effect of measurement error" (Jensen, 1998), a phenomenon known as regression dilution.

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Correlation and dependence

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.

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Correlation function

A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables.

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Coskewness

In probability theory and statistics, coskewness is a measure of how much three random variables change together.

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Count data

In statistics, count data is a statistical data type, a type of data in which the observations can take only the non-negative integer values, and where these integers arise from counting rather than ranking.

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Coupon collector's problem

In probability theory, the coupon collector's problem describes the "collect all coupons and win" contests.

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Covariance

In probability theory and statistics, covariance is a measure of the joint variability of two random variables.

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Covariance and correlation

In probability theory and statistics, the mathematical concepts of covariance and correlation are very similar.

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Covariance mapping

In statistics, covariance mapping is an extension of the covariance concept from random variables to random functions.

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Covariance matrix

In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.

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Cramér's theorem (large deviations)

Cramér's theorem is a fundamental result in the theory of large deviations, a subdiscipline of probability theory.

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Cramér–Rao bound

In estimation theory and statistics, the Cramér–Rao bound (CRB), Cramér–Rao lower bound (CRLB), Cramér–Rao inequality, Frechet–Darmois–Cramér–Rao inequality, or information inequality expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter.

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Cramér’s decomposition theorem

In mathematical statistics, Cramér's theorem (or Cramér’s decomposition theorem) is one of several theorems of Harald Cramér, a Swedish statistician and probabilist.

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Cross entropy

In information theory, the cross entropy between two probability distributions p and q over the same underlying set of events measures the average number of bits needed to identify an event drawn from the set, if a coding scheme is used that is optimized for an "unnatural" probability distribution q, rather than the "true" distribution p. The cross entropy for the distributions p and q over a given set is defined as follows: where H(p) is the entropy of p, and D_(p \| q) is the Kullback–Leibler divergence of q from p (also known as the relative entropy of p with respect to q — note the reversal of emphasis).

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Cross-correlation

In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.

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Cumulant

In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Cylindrical σ-algebra

In mathematics — specifically, in measure theory and functional analysis — the cylindrical σ-algebra is a σ-algebra often used in the study either product measure or probability measure of random variables on Banach spaces.

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Data transformation (statistics)

In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set — that is, each data point zi is replaced with the transformed value yi.

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Data validation and reconciliation

Industrial process data validation and reconciliation, or more briefly, data validation and reconciliation (DVR), is a technology that uses process information and mathematical methods in order to automatically correct measurements in industrial processes.

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Datar–Mathews method for real option valuation

The Datar–Mathews method (DM method) is a method for real options valuation.

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De Finetti's theorem

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some latent variable.

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Decoupling (probability)

In probability and statistics, decoupling is a reduction of a sample statistic to an average of the statistic evaluated on several independent sequences of the random variable.

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Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

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Degenerate distribution

In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension.

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

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Determining the number of clusters in a data set

Determining the number of clusters in a data set, a quantity often labelled k as in the ''k''-means algorithm, is a frequent problem in data clustering, and is a distinct issue from the process of actually solving the clustering problem.

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Deterministic simulation

In mathematical modeling, deterministic simulations contain no random variables and no degree of randomness, and consist mostly of equations, for example difference equations.

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Deviation risk measure

In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure.

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DEVS

DEVS abbreviating Discrete Event System Specification is a modular and hierarchical formalism for modeling and analyzing general systems that can be discrete event systems which might be described by state transition tables, and continuous state systems which might be described by differential equations, and hybrid continuous state and discrete event systems.

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Differential entropy

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions.

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Dirichlet distribution

In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted \operatorname(\boldsymbol\alpha), is a family of continuous multivariate probability distributions parameterized by a vector \boldsymbol\alpha of positive reals.

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Dirichlet process

In probability theory, Dirichlet processes (after Peter Gustav Lejeune Dirichlet) are a family of stochastic processes whose realizations are probability distributions.

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Discrete event simulation

A discrete-event simulation (DES) models the operation of a system as a discrete sequence of events in time.

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Distance correlation

In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension.

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Distortion function

A distortion function g: \to is a non-decreasing function such that g(0).

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Distortion risk measure

In financial mathematics, a distortion risk measure is a type of risk measure which is related to the cumulative distribution function of the return of a financial portfolio.

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Distribution ensemble

In cryptography, a distribution ensemble or probability ensemble is a family of distributions or random variables X.

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Dobiński's formula

In combinatorial mathematics, Dobiński’s formula states that the n-th Bell number Bn (i.e., the number of partitions of a set of size n) equals The formula is named after G. Dobiński, who published it in 1877.

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Dominated convergence theorem

In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm.

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Donsker's theorem

In probability theory, Donsker's theorem (also known as Donsker's invariance principle, or the functional central limit theorem), named after Monroe D. Donsker, is a functional extension of the central limit theorem.

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Doob martingale

A Doob martingale (also known as a Levy martingale) is a mathematical construction of a stochastic process which approximates a given random variable and has the martingale property with respect to the given filtration.

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Doob's martingale convergence theorems

In mathematicsspecifically, in the theory of stochastic processesDoob's martingale convergence theorems are a collection of results on the long-time limits of supermartingales, named after the American mathematician Joseph L. Doob.

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Doob's martingale inequality

In mathematics, Doob's martingale inequality is a result in the study of stochastic processes.

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Doob–Dynkin lemma

In probability theory, the Doob–Dynkin lemma, named after Joseph L. Doob and Eugene Dynkin, characterizes the situation when one random variable is a function of another by the inclusion of the \sigma-algebras generated by the random variables.

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Drainage research

Drainage research is the study of agricultural drainage systems and their effects to arrive at optimal system design.

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Dual total correlation

In information theory, dual total correlation (Han 1978), excess entropy (Olbrich 2008), or binding information (Abdallah and Plumbley 2010) is one of the two known non-negative generalizations of mutual information.

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Dvoretzky–Kiefer–Wolfowitz inequality

In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz inequality predicts how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn.

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Dynamic risk measure

In financial mathematics, a conditional risk measure is a random variable of the financial risk (particularly the downside risk) as if measured at some point in the future.

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Dynamic scaling

Dynamic scaling (sometimes known as Family-Vicsek scaling) is the litmus test of showing that an evolving system exhibits self-similarity.

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Eaton's inequality

In probability theory, Eaton's inequality is a bound on the largest values of a linear combination of bounded random variables.

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Econometric model

Econometric models are statistical models used in econometrics.

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Electronic engineering

Electronic engineering (also called electronics and communications engineering) is an electrical engineering discipline which utilizes nonlinear and active electrical components (such as semiconductor devices, especially transistors, diodes and integrated circuits) to design electronic circuits, devices, VLSI devices and their systems.

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Elementary event

In probability theory, an elementary event (also called an atomic event or simple event) is an event which contains only a single outcome in the sample space.

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Elo rating system

The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess.

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Empirical measure

In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables.

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Empirical risk minimization

Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on their performance.

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Entropic value at risk

In financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a random outcome or risk position.

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Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

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Entropy power inequality

In information theory, the entropy power inequality is a result that relates to so-called "entropy power" of random variables.

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Equals sign

The equals sign or equality sign is a mathematical symbol used to indicate equality.

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Equicontinuity

In mathematical analysis, a family of functions is equicontinuous if all the functions are continuous and they have equal variation over a given neighbourhood, in a precise sense described herein.

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Erdős–Tetali theorem

In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive basis of every order.

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Ergodic sequence

In mathematics, an ergodic sequence is a certain type of integer sequence, having certain equidistribution properties.

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Error function

In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.

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Estimation of covariance matrices

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated.

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Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.

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Euler–Maruyama method

In Itô calculus, the Euler–Maruyama method (also called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE).

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Event (probability theory)

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

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Evolutionary economics

Evolutionary economics is part of mainstream economics as well as a heterodox school of economic thought that is inspired by evolutionary biology.

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Exchangeable random variables

In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence such that future observations behave like earlier observations.

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Expectation–maximization algorithm

In statistics, an expectation–maximization (EM) algorithm is an iterative method to find maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables.

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Expected return

The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment).

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Experimental uncertainty analysis

Experimental uncertainty analysis is a technique that analyses a derived quantity, based on the uncertainties in the experimentally measured quantities that are used in some form of mathematical relationship ("model") to calculate that derived quantity.

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Exponential distribution

No description.

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Exponential-logarithmic distribution

No description.

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Extreme value theory

Extreme value theory or extreme value analysis (EVA) is a branch of statistics dealing with the extreme deviations from the median of probability distributions.

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F-distribution

No description.

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Fabius function

In mathematics, the Fabius function is an example of an infinitely differentiable function that is nowhere analytic, found by.

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Factorial code

Most real world data sets consist of data vectors whose individual components are not statistically independent.

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Factorial moment

In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable.

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Factorial moment generating function

In probability theory and statistics, the factorial moment generating function of the probability distribution of a real-valued random variable X is defined as for all complex numbers t for which this expected value exists.

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Factorial moment measure

In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.

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Fano factor

In statistics, the Fano factor, like the coefficient of variation, is a measure of the dispersion of a probability distribution of a Fano noise.

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Fano's inequality

In information theory, Fano's inequality (also known as the Fano converse and the Fano lemma) relates the average information lost in a noisy channel to the probability of the categorization error.

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Fat-tailed distribution

A fat-tailed distribution is a probability distribution that has the property, along with the other heavy-tailed distributions, that it exhibits large skewness or kurtosis.

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Fatou's lemma

In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions.

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Fernique's theorem

In mathematics — specifically, in measure theory — Fernique's theorem is a result about Gaussian measures on Banach spaces.

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Field (physics)

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space and time.

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Filtering problem (stochastic processes)

In the theory of stochastic processes, the filtering problem is a mathematical model for a number of state estimation problems in signal processing and related fields.

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Finite-valued logic

In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete.

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Fisher information

In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.

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Fisher information metric

In information geometry, the Fisher information metric is a particular Riemannian metric which can be defined on a smooth statistical manifold, i.e., a smooth manifold whose points are probability measures defined on a common probability space.

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Fisher's noncentral hypergeometric distribution

In probability theory and statistics, Fisher's noncentral hypergeometric distribution is a generalization of the hypergeometric distribution where sampling probabilities are modified by weight factors.

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Fisher–Tippett–Gnedenko theorem

In statistics, the Fisher–Tippett–Gnedenko theorem (also the Fisher–Tippett theorem or the extreme value theorem) is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics.

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Flory–Huggins solution theory

Flory–Huggins solution theory is a mathematical model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing.

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Flow (mathematics)

In mathematics, a flow formalizes the idea of the motion of particles in a fluid.

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Folded normal distribution

No description.

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Force of mortality

In actuarial science, force of mortality represents the instantaneous rate of mortality at a certain age measured on an annualized basis.

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Forward volatility

Forward volatility is a measure of the implied volatility of a financial instrument over a period in the future, extracted from the term structure of volatility (which refers to how implied volatility differs for related financial instruments with different maturities).

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Franck Barthe

Franck Barthe is a French mathematician.

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Free parameter

A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model and must be estimated experimentally or theoretically.

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Free probability

Free probability is a mathematical theory that studies non-commutative random variables.

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Free product

In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result contains both G and H as subgroups, is generated by the elements of these subgroups, and is the “most general” group having these properties.

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Functional derivative

In the calculus of variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional to a change in a function on which the functional depends.

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Fuzzy number

A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1.

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Galton–Watson process

The Galton–Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names.

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Gamma distribution

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

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Gauss's inequality

In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode.

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Gauss–Kuzmin distribution

In mathematics, the Gauss–Kuzmin distribution is a discrete probability distribution that arises as the limit probability distribution of the coefficients in the continued fraction expansion of a random variable uniformly distributed in (0, 1).

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Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form: for arbitrary real constants, and.

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Gaussian process

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed.

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Generalized integer gamma distribution

In probability and statistics, the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters and different rate parameters.

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Generalized linear model

In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution.

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Generalized minimum-distance decoding

In coding theory, generalized minimum-distance (GMD) decoding provides an efficient algorithm for decoding concatenated codes, which is based on using an errors-and-erasures decoder for the outer code.

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Generating function

In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.

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Geometric Brownian motion

A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift.

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Geometric distribution

In probability theory and statistics, the geometric distribution is either of two discrete probability distributions.

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Geostatistics

Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets.

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Gibbs measure

In mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics.

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Gibbs sampling

In statistics, Gibbs sampling or a Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm for obtaining a sequence of observations which are approximated from a specified multivariate probability distribution, when direct sampling is difficult.

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Giuseppe Pompilj

Giuseppe Pompilj (17 July 1913, Rome–9 July 1968, Rome) was an Italian statistician.

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Glossary of probability and statistics

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself.

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Gompertz–Makeham law of mortality

The Gompertz–Makeham law states that the human death rate is the sum of an age-independent component (the Makeham term, named after William Makeham) and an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age.

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Gradsect

A gradsect or gradient-directed transect is a low-input, high-return sampling method where the aim is to maximise information about the distribution of biota in any area of study.

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Gramian matrix

In linear algebra, the Gram matrix (Gramian matrix or Gramian) of a set of vectors v_1,\dots, v_n in an inner product space is the Hermitian matrix of inner products, whose entries are given by G_.

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Graphical model

A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables.

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Graphical models for protein structure

Graphical models have become powerful frameworks for protein structure prediction, protein–protein interaction and free energy calculations for protein structures.

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Greek letters used in mathematics, science, and engineering

Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.

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Group family

In probability theory, especially as that field is used in statistics, a group family of probability distributions is a family obtained by subjecting a random variable with a fixed distribution to a suitable family of transformations such as a location-scale family, or otherwise a family of probability distributions acted upon by a group.

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Gumbel distribution

In probability theory and statistics, the Gumbel distribution (Generalized Extreme Value distribution Type-I) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions.

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Haar wavelet

In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis.

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Half-logistic distribution

No description.

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Hamburger moment problem

In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence, does there exist a positive Borel measure μ (for instance, the cumulative distribution function of a random variable) on the real line such that In other words, an affirmative answer to the problem means that is the sequence of moments of some positive Borel measure μ.

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Harmonic distribution

In probability theory and statistics, the harmonic distribution is a continuous probability distribution.

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Harmonic series (mathematics)

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.

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Hash table

In computing, a hash table (hash map) is a data structure that implements an associative array abstract data type, a structure that can map keys to values.

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Hausdorff moment problem

In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments of some Borel measure μ supported on the closed unit interval.

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Hölder's inequality

In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces.

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Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by or (but sometimes, or), is a discontinuous function named after Oliver Heaviside (1850–1925), whose value is zero for negative argument and one for positive argument.

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Heavy-tailed distribution

In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution.

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Helly–Bray theorem

In probability theory, the Helly–Bray theorem relates the weak convergence of cumulative distribution functions to the convergence of expectations of certain measurable functions.

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Herbert Robbins

Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician.

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Hermite distribution

In probability theory and statistics, the Hermite distribution, named after Charles Hermite, is a discrete probability distribution used to model count data with more than one parameter.

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Hermite polynomials

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.

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Heteroscedasticity

In statistics, a collection of random variables is heteroscedastic (or heteroskedastic; from Ancient Greek hetero “different” and skedasis “dispersion”) if there are sub-populations that have different variabilities from others.

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Highly optimized tolerance

In applied mathematics, highly optimized tolerance (HOT) is a method of generating power law behavior in systems by including a global optimization principle.

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History of mathematical notation

The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness.

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Hitting time

In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space.

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Hoeffding's inequality

In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount.

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Hoeffding's lemma

In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable.

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Holevo's theorem

Holevo's theorem is an important limitative theorem in quantum computing, an interdisciplinary field of physics and computer science.

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Homoscedasticity

In statistics, a sequence or a vector of random variables is homoscedastic if all random variables in the sequence or vector have the same finite variance.

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Hotelling's T-squared distribution

In statistics Hotelling's T-squared distribution (T2) is a multivariate distribution proportional to the ''F''-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution.

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Hsu–Robbins–Erdős theorem

In the mathematical theory of probability, the Hsu–Robbins–Erdős theorem states that if X_1, \ldots,X_n is a sequence of i.i.d. random variables with zero mean and finite variance and then for every \varepsilon > 0.

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Hugo Steinhaus

Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Jewish-Polish mathematician and educator.

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Hyperbolic absolute risk aversion

In finance, economics, and decision theory, hyperbolic absolute risk aversion (HARA) (Chapter I of his Ph.D. dissertation; Chapter 5 in his Continuous-Time Finance).

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Hyperbolic secant distribution

In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function.

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Hyperexponential distribution

In probability theory, a hyperexponential distribution is a continuous probability distribution whose probability density function of the random variable X is given by where each Yi is an exponentially distributed random variable with rate parameter λi, and pi is the probability that X will take on the form of the exponential distribution with rate λi.

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Hypergeometric distribution

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure.

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Illustration of the central limit theorem

This article gives two concrete illustrations of the central limit theorem.

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Importance sampling

In statistics, importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest.

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Imprecise Dirichlet process

In probability theory and statistics, the Dirichlet process (DP) is one of the most popular Bayesian nonparametric models.

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Increasing process

An increasing process is a stochastic process where the random variables X_t which make up the process are increasing almost surely and adapted: A continuous increasing process is such a process where the set M is continuous.

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Indecomposable distribution

In probability theory, an indecomposable distribution is a probability distribution that cannot be represented as the distribution of the sum of two or more non-constant independent random variables: Z ≠ X + Y.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

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Independent Reference Model

The Independent Reference Model (I.R.M) is a conceptual model used in the analysis of storage system: disk drives, caches, etc.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

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Inequalities in information theory

Inequalities are very important in the study of information theory.

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Infinite divisibility

Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics).

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Infinite divisibility (probability)

In probability theory, a probability distribution is infinitely divisible if it can be expressed as the probability distribution of the sum of an arbitrary number of independent and identically distributed random variables.

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Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

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Info-metrics

Info-metrics is an interdisciplinary approach to scientific modeling, inference and efficient information processing.

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Information bottleneck method

The information bottleneck method is a technique in information theory introduced by Naftali Tishby, Fernando C. Pereira, and William Bialek.

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Information coefficient

The information coefficient (IC) is a measure of the merit of a predicted value.

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Information geometry

Information geometry is a branch of mathematics that applies the techniques of differential geometry to the field of probability theory.

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Information source (mathematics)

In mathematics, an information source is a sequence of random variables ranging over a finite alphabet Γ, having a stationary distribution.

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Information theory

Information theory studies the quantification, storage, and communication of information.

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Information theory and measure theory

This article discusses how information theory (a branch of mathematics studying the transmission, processing and storage of information) is related to measure theory (a branch of mathematics related to integration and probability).

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Inner product space

In linear algebra, an inner product space is a vector space with an additional structure called an inner product.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Interaction (statistics)

In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive.

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Internal rate of return

The internal rate of return (IRR) is a method of calculating rate of return.

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Intertemporal portfolio choice

Intertemporal portfolio choice is the process of allocating one's investable wealth to various assets, especially financial assets, repeatedly over time, in such a way as to optimize some criterion.

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Invariant (mathematics)

In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.

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Invariant estimator

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity.

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Invariant measure

In mathematics, an invariant measure is a measure that is preserved by some function.

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Inverse Gaussian distribution

In probability theory, the inverse Gaussian distribution (also known as the Wald distribution) is a two-parameter family of continuous probability distributions with support on (0,∞).

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Inverse transform sampling

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, golden ruleAalto University, N. Hyvönen, Computational methods in inverse problems. Twelfth lecture https://noppa.tkk.fi/noppa/kurssi/mat-1.3626/luennot/Mat-1_3626_lecture12.pdf) is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its cumulative distribution function.

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Inverse-variance weighting

In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average.

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Irwin–Hall distribution

In probability and statistics, the Irwin–Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a uniform distribution.

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Isotropic measure

In probability theory, an isotropic measure is any mathematical measure that is invariant under linear isometries.

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Itô calculus

Itô calculus, named after Kiyoshi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process).

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J. Laurie Snell

James Laurie Snell, often cited as J. Laurie Snell, (January 15, 1925 in Wheaton, Illinois – March 19, 2011 in Hanover, New Hampshire) was an American mathematician.

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James–Stein estimator

The James–Stein estimator is a biased estimator of the mean of Gaussian random vectors.

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Jamshidian's trick

Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option on a portfolio of assets as a portfolio of options.

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János Komlós (mathematician)

János Komlós (Budapest, 23 May 1942) is a Hungarian-American mathematician, working in probability theory and discrete mathematics.

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Jensen's inequality

In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

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Johan de Witt

Johan de Witt or Jan de Witt, heer van Zuid- en Noord-Linschoten, Snelrewaard, Hekendorp and IJsselveere (24 September 1625 – 20 August 1672) was a key figure in Dutch politics in the mid-17th century, when its flourishing sea trade in a period of globalisation made the United Provinces a leading European power during the Dutch Golden Age.

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John Gordon Skellam

John Gordon Skellam (1914-1979) was a statistician and ecologist, who discovered the Skellam distribution.

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John Muth

John Fraser Muth (September 27, 1930 – October 23, 2005) was an American economist.

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Johnson's SU-distribution

The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949.

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Joint entropy

In information theory, joint entropy is a measure of the uncertainty associated with a set of variables.

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Joint probability distribution

Given random variables X, Y,..., that are defined on a probability space, the joint probability distribution for X, Y,...

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Joint quantum entropy

The joint quantum entropy generalizes the classical joint entropy to the context of quantum information theory.

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K-distribution

In probability and statistics, the K-distribution is a three-parameter family of continuous probability distributions.

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Karhunen–Loève theorem

In the theory of stochastic processes, the Karhunen–Loève theorem (named after Kari Karhunen and Michel Loève), also known as the Kosambi–Karhunen–Loève theorem is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function on a bounded interval.

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Kernel (statistics)

The term kernel is a term in statistical analysis used to refer to a window function.

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Kernel density estimation

In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.

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Kernel regression

Kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable.

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Khintchine inequality

In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Roman alphabet, is a theorem from probability, and is also frequently used in analysis.

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Kingman's subadditive ergodic theorem

In mathematics, Kingman's subadditive ergodic theorem is one of several ergodic theorems.

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Kolmogorov's inequality

In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound.

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Kolmogorov's three-series theorem

In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions.

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Kolmogorov's zero–one law

In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, called a tail event, will either almost surely happen or almost surely not happen; that is, the probability of such an event occurring is zero or one.

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Kolmogorov–Smirnov test

In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous, one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two samples (two-sample K–S test).

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Komlós–Major–Tusnády approximation

In theory of probability, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) is an approximation of the empirical process by a Gaussian process constructed on the same probability space.

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Kriging

In statistics, originally in geostatistics, kriging or Gaussian process regression is a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances, as opposed to a piecewise-polynomial spline chosen to optimize smoothness of the fitted values.

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Kubilius model

In mathematics, the Kubilius model relies on a clarification and extension of a finite probability space on which the behaviour of additive arithmetic functions can be modeled by sum of independent random variables.

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Kuiper's test

Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data.

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Kumaraswamy distribution

In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval.

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Kurtosis

In probability theory and statistics, kurtosis (from κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable.

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Langevin dynamics

In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist Paul Langevin.

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Laplace distribution

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

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Laplace functional

In probability theory, a Laplace functional refers to one of two possible mathematical functions of functions or, more precisely, functionals that serve as mathematical tools for studying either point processes or concentration of measure properties of metric spaces.

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Laplace principle (large deviations theory)

In mathematics, Laplace's principle is a basic theorem in large deviations theory, similar to Varadhan's lemma.

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Laplace transform

In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.

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Laplace–Stieltjes transform

The Laplace–Stieltjes transform, named for Pierre-Simon Laplace and Thomas Joannes Stieltjes, is an integral transform similar to the Laplace transform.

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Large deviations theory

In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions.

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Latin letters used in mathematics

Many letters of the Latin alphabet, both capital and small, are used in mathematics, science and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, physical entities.

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Law of large numbers

In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times.

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Law of the iterated logarithm

In probability theory, the law of the iterated logarithm describes the magnitude of the fluctuations of a random walk.

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Law of the unconscious statistician

In probability theory and statistics, the law of the unconscious statistician (sometimes abbreviated LOTUS) is a theorem used to calculate the expected value of a function g(X) of a random variable X when one knows the probability distribution of X but one does not explicitly know the distribution of g(X).

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Law of total covariance

In probability theory, the law of total covariance, covariance decomposition formula, or conditional covariance formual states that if X, Y, and Z are random variables on the same probability space, and the covariance of X and Y is finite, then The nomenclature in this article's title parallels the phrase law of total variance.

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Law of total cumulance

In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance.

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Law of total expectation

The proposition in probability theory known as the law of total expectation, the law of iterated expectations, the tower rule, and the smoothing theorem, among other names, states that if X is a random variable whose expected value \operatorname(X) is defined, and Y is any random variable on the same probability space, then i.e., the expected value of the conditional expected value of X given Y is the same as the expected value of X. One special case states that if _i is a finite or countable partition of the sample space, then.

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Law of total probability

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities.

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Law of total variance

In probability theory, the law of total variance or variance decomposition formula or conditional variance formulas or Law of Iterated Variances also known as Eve's law, states that if X and Y are random variables on the same probability space, and the variance of Y is finite, then \operatorname(Y).

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Lévy distribution

No description.

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Lévy metric

In mathematics, the Lévy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables.

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Lévy process

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length.

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Lévy's continuity theorem

To probability theory, Lévy’s continuity theorem (or Lévy's convergence theoremWilliams (1991, section 18.1)), named after the French mathematician Paul Lévy, connects convergence in distribution of the sequence of random variables with pointwise convergence of their characteristic functions.

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Le Cam's theorem

In probability theory, Le Cam's theorem, named after Lucien le Cam (1924 – 2000), states the following.

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Leftover hash lemma

The leftover hash lemma is a lemma in cryptography first stated by Russell Impagliazzo, Leonid Levin, and Michael Luby.

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Lehmer code

In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers.

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Leibniz integral rule

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form where -\infty, the derivative of this integral is expressible as where the partial derivative indicates that inside the integral, only the variation of f(x, t) with x is considered in taking the derivative.

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Likelihood function

In frequentist inference, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.

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Likelihood principle

In statistics, the likelihood principle is that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function.

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Lindeberg's condition

In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit theorem (CLT) to hold for a sequence of independent random variables.

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Line sampling

Line sampling is a method used in reliability engineering to compute small (i.e., rare event) failure probabilities encountered in engineering systems.

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.

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Linear predictor function

In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable.

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Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

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Linear trend estimation

Trend estimation is a statistical technique to aid interpretation of data.

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List of convolutions of probability distributions

In probability theory, the probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions.

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List of letters used in mathematics and science

Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.

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List of mathematical abbreviations

This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology.

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List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

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List of matrices

This page lists some important classes of matrices used in mathematics, science and engineering.

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List of probability distributions

Many probability distributions that are important in theory or applications have been given specific names.

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List of probability topics

This is a list of probability topics, by Wikipedia page.

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List of statistics articles

No description.

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Locally convex topological vector space

In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.

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Location–scale family

In probability theory, especially in mathematical statistics, a location–scale family is a family of probability distributions parametrized by a location parameter and a non-negative scale parameter.

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Log-Cauchy distribution

In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution.

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Log-Laplace distribution

In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution.

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Log-logistic distribution

No description.

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Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Logarithmic distribution

In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the Maclaurin series expansion From this we obtain the identity This leads directly to the probability mass function of a Log(p)-distributed random variable: for k ≥ 1, and where 0 F(k).

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Logarithmically concave function

In convex analysis, a non-negative function is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all and.

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Logistic distribution

In probability theory and statistics, the logistic distribution is a continuous probability distribution.

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Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that is usually taken to apply to a binary dependent variable.

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Logit-normal distribution

In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution.

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Long-tail traffic

A long-tailed or heavy-tailed probability distribution is one that assigns relatively high probabilities to regions far from the mean or median.

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Lorden's inequality

In probability theory, Lorden's inequality is a bound for the moments of overshoot for a stopped sum of random variables, first published by Gary Lorden in 1970.

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Loss reserving

Loss reserving refers to the calculation of the required reserves for a tranche of general insurance business.

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Low-rank matrix approximations

Low-rank matrix approximations are essential tools in the application of kernel methods to large-scale learning problems.

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Lukacs's proportion-sum independence theorem

In statistics, Lukacs's proportion-sum independence theorem is a result that is used when studying proportions, in particular the Dirichlet distribution.

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M/G/1 queue

In queueing theory, a discipline within the mathematical theory of probability, an M/G/1 queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a General distribution and there is a single server.

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M/G/k queue

In queueing theory, a discipline within the mathematical theory of probability, an M/G/k queue is a queue model where arrivals are Markovian (modulated by a Poisson process), service times have a General distribution and there are k servers.

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Machine learning

Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.

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Malliavin calculus

In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes.

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Marchenko–Pastur distribution

The red line is the standard normal distribution --> In the mathematical theory of random matrices, the Marchenko–Pastur distribution, or Marchenko–Pastur law, describes the asymptotic behavior of singular values of large rectangular random matrices.

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Margin of error

The margin of error is a statistic expressing the amount of random sampling error in a survey's results.

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Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.

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Marginal likelihood

In statistics, a marginal likelihood function, or integrated likelihood, is a likelihood function in which some parameter variables have been marginalized.

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Markov chain

A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".

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Markov information source

In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.

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Markov kernel

In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that plays the role, in the general theory of Markov processes, that the transition matrix does in the theory of Markov processes with a finite state space.

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Markov model

In probability theory, a Markov model is a stochastic model used to model randomly changing systems.

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Markov property

In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process.

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Markov random field

In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph.

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Markov's inequality

In probability theory, Markov's inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant.

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Marsaglia polar method

The polar method (attributed to George Marsaglia, 1964) is a pseudo-random number sampling method for generating a pair of independent standard normal random variables.

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Marshall–Olkin exponential distribution

No description.

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Martin Beale

Evelyn Martin Lansdowne Beale FRS (8 September 1928 – 23 December 1985) was an applied mathematician and statistician who was one of the pioneers of mathematical programming.

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Martingale (probability theory)

In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values.

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Mathematical and theoretical biology

Mathematical and theoretical biology is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories.

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Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

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Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

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Mathematical statistics

Mathematical statistics is the application of mathematics to statistics, as opposed to techniques for collecting statistical data.

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Matrix (mathematics)

In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution.

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Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions.

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Maximum entropy thermodynamics

In physics, maximum entropy thermodynamics (colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes.

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Maxwell's theorem

In probability theory, Maxwell's theorem, named in honor of James Clerk Maxwell, states that if the probability distribution of a vector-valued random variable X.

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McCullagh's parametrization of the Cauchy distributions

In probability theory, the "standard" Cauchy distribution is the probability distribution whose probability density function (pdf) is for x real.

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Mean

In mathematics, mean has several different definitions depending on the context.

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Mean absolute difference

The mean absolute difference (univariate) is a measure of statistical dispersion equal to the average absolute difference of two independent values drawn from a probability distribution.

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Mean absolute error

In statistics, mean absolute error (MAE) is a measure of difference between two continuous variables.

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Mean dependence

In probability theory, a random variable Y is said to be mean independent of random variable X if and only if its conditional mean E(Y | X.

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Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and what is estimated.

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Mean value theorem

In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

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Measurable function

In mathematics and in particular measure theory, a measurable function is a function between two measurable spaces such that the preimage of any measurable set is measurable, analogously to the definition that a function between topological spaces is continuous if the preimage of each open set is open.

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Measurement uncertainty

In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity.

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Median

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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Memorylessness

In probability and statistics, memorylessness is a property of certain probability distributions.

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Metaheuristic

In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity.

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Method of moments (probability theory)

In probability theory, the method of moments is a way of proving convergence in distribution by proving convergence of a sequence of moment sequences.

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Method of moments (statistics)

In statistics, the method of moments is a method of estimation of population parameters.

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Metropolis–Hastings algorithm

In statistics and in statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution for which direct sampling is difficult.

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Mills ratio

In probability theory, the Mills ratio (or Mills's ratio) of a continuous random variable X is the function where f(x) is the probability density function, and is the complementary cumulative distribution function (also called survival function).

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MinHash

In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are.

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Minimum chi-square estimation

In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data.

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Minimum distance estimation

Minimum distance estimation (MDE) is a statistical method for fitting a mathematical model to data, usually the empirical distribution.

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Mixed Poisson process

In probability theory, a mixed Poisson process is a special point process that is a generalization of a Poisson process.

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Mixing (mathematics)

In mathematics, mixing is an abstract concept originating from physics: the attempt to describe the irreversible thermodynamic process of mixing in the everyday world: mixing paint, mixing drinks, etc.

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Mixture distribution

In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.

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Mode (statistics)

The mode of a set of data values is the value that appears most often.

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Moderation (statistics)

In statistics and regression analysis, moderation occurs when the relationship between two variables depends on a third variable.

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Modified lognormal power-law distribution

The Modified Lognormal Power-Law (MLP) function is a three parameter function that can be used to model data that have characteristics of a log-normal distribution and a power law behavior.

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Moment (mathematics)

In mathematics, a moment is a specific quantitative measure, used in both mechanics and statistics, of the shape of a set of points.

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Moment measure

In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.

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Moment-generating function

In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.

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Monetary conditions index

In macroeconomics, a monetary conditions index (MCI) is an index number calculated from a linear combination of a small number of economy-wide financial variables deemed relevant for monetary policy.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Multidimensional Chebyshev's inequality

In probability theory, the multidimensional Chebyshev's inequality is a generalization of Chebyshev's inequality, which puts a bound on the probability of the event that a random variable differs from its expected value by more than a specified amount.

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Multifactor dimensionality reduction

Multifactor dimensionality reduction (MDR) is a statistical approach, also used in machine learning automatic approaches, for detecting and characterizing combinations of attributes or independent variables that interact to influence a dependent or class variable.

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Multilevel model

Multilevel models (also known as hierarchical linear models, nested data models, mixed models, random coefficient, random-effects models, random parameter models, or split-plot designs) are statistical models of parameters that vary at more than one level.

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Multilevel Monte Carlo method

Multilevel Monte Carlo (MLMC) methods in numerical analysis are algorithms for computing expectations that arise in stochastic simulations.

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Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes.

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Multivariate mutual information

In information theory there have been various attempts over the years to extend the definition of mutual information to more than two random variables.

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Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

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Multivariate random variable

In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.

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Multivariate t-distribution

In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution.

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Mutation (genetic algorithm)

Mutation is a genetic operator used to maintain genetic diversity from one generation of a population of genetic algorithm chromosomes to the next.

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Mutual information

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables.

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Naive Bayes spam filtering

Naive Bayes classifiers are a popular statistical technique of e-mail filtering.

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Negative binomial distribution

In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

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Negative hypergeometric distribution

In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail, Male/Female or Employed/Unemployed.

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Negative probability

The probability of the outcome of an experiment is never negative, but quasiprobability distributions can be defined that allow a negative probability, or quasiprobability for some events.

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Neutral vector

In statistics, and specifically in the study of the Dirichlet distribution, a neutral vector of random variables is one that exhibits a particular type of statistical independence amongst its elements.

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Newsvendor model

The newsvendor (or newsboy or single-periodWilliam J. Stevenson, Operations Management. 10th edition, 2009; page 581 or perishable) model is a mathematical model in operations management and applied economics used to determine optimal inventory levels.

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No free lunch in search and optimization

In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method.

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Nonparametric skew

In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Normal-gamma distribution

In probability theory and statistics, the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions.

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Normal-inverse Gaussian distribution

The normal-inverse Gaussian distribution (NIG) is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the inverse Gaussian distribution.

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Normality test

In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.

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Normally distributed and uncorrelated does not imply independent

In probability theory, two random variables being linearly uncorrelated does not imply their independence (however, for some measures of non-linear correlation such as the distance correlation, uncorrelated implies independent).

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Notation in probability and statistics

Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols.

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Nuisance variable

In the theory of stochastic processes in probability theory and statistics, a nuisance variable is a random variable that is fundamental to the probabilistic model, but that is of no particular interest in itself or is no longer of interest: one such usage arises for the Chapman–Kolmogorov equation.

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Object categorization from image search

In computer vision, the problem of object categorization from image search is the problem of training a classifier to recognize categories of objects, using only the images retrieved automatically with an Internet search engine.

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Oblivious ram

An Oblivious RAM (ORAM) simulator is a compiler that transforms algorithms in such a way that the resulting algorithms preserve the input-output behavior of the original algorithm but the distribution of memory access pattern of the transformed algorithm is independent of the memory access pattern of the original algorithm.

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Observational error

Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.

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Observed information

In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function).

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Occupancy grid mapping

Occupancy Grid Mapping refers to a family of computer algorithms in probabilistic robotics for mobile robots which address the problem of generating maps from noisy and uncertain sensor measurement data, with the assumption that the robot pose is known.

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Odds

Odds are a numerical expression, usually expressed as a pair of numbers, used in both gambling and statistics.

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Odds ratio

In statistics, the odds ratio (OR) is one of three main ways to quantify how strongly the presence or absence of property A is associated with the presence or absence of property B in a given population.

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Omitted-variable bias

In statistics, omitted-variable bias (OVB) occurs when a statistical model incorrectly leaves out one or more relevant variables.

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On the Freedom of the Will

On the Freedom of the Will (Ueber die Freiheit des menschlichen Willens) is an essay presented to the Royal Norwegian Society of Sciences in 1839 by Arthur Schopenhauer as a response to the academic question that they had posed: "Is it possible to demonstrate human free will from self-consciousness?" It is one of the constituent essays of his work Die beiden Grundprobleme der Ethik.

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Optimal decision

An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options.

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Order and disorder

In physics, the terms order and disorder designate the presence or absence of some symmetry or correlation in a many-particle system.

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Outage probability

In Information theory, outage probability of a communication channel is the probability that a given information rate is not supported, because of variable channel capacity.

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Outcome (probability)

In probability theory, an outcome is a possible result of an experiment.

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Outer product

In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.

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Outline of discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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Outline of epistemology

The following outline is provided as an overview of and topical guide to epistemology: Epistemology or theory of knowledge – branch of philosophy concerned with the nature and scope of knowledge.

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Outline of probability

Probability is a measure of the likeliness that an event will occur.

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Outline of statistics

Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data.

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Owen's T function

In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by The function was first introduced by Owen in 1956.

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P-rep

In statistical hypothesis testing, p-rep or prep has been proposed as a statistical to the classic p-value.

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P-value

In statistical hypothesis testing, the p-value or probability value or asymptotic significance is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.

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Pafnuty Chebyshev

Pafnuty Lvovich Chebyshev (p) (–) was a Russian mathematician.

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Pairwise error probability

Pairwise error probability is the error probability that for a transmitted signal (X) its corresponding but distorted version (\widehat) will be received.

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Pairwise independence

In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent.

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Paley–Zygmund inequality

In mathematics, the Paley–Zygmund inequality bounds the probability that a positive random variable is small, in terms of its mean and variance (i.e., its first two moments).

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Panjer recursion

The Panjer recursion is an algorithm to compute the probability distribution approximation of a compound random variable S.

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Parameter

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

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Pareto distribution

No description.

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Pareto interpolation

Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution.

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Partial correlation

In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed.

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Partition function (mathematics)

The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics.

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Partition function (quantum field theory)

In quantum field theory, the partition function Z is the generating functional of all correlation functions, generalizing the characteristic function of probability theory.

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Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

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Path coefficient

Path coefficients are standardized versions of linear regression weights which can be used in examining the possible causal linkage between statistical variables in the structural equation modeling approach.

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Perplexity

In information theory, perplexity is a measurement of how well a probability distribution or probability model predicts a sample.

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Phase-shift keying

Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave).

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Phase-type distribution

No description.

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Pi

The number is a mathematical constant.

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Pi-system

In mathematics, a -system (or pi-system) on a set Ω is a collection P of certain subsets of Ω, such that.

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Pickands–Balkema–de Haan theorem

The Pickands–Balkema–de Haan theorem is often called the second theorem in extreme value theory.

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Pigeonhole principle

In mathematics, the pigeonhole principle states that if items are put into containers, with, then at least one container must contain more than one item.

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Point particle

A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.

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Point process

In statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on some underlying mathematical space such as the real line, the Cartesian plane, or more abstract spaces.

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Point process notation

In probability and statistics, point process notation comprises the range of mathematical notation used to symbolically represent random objects known as point processes, which are used in related fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable as points, in time, space or both.

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Pointwise mutual information

Pointwise mutual information (PMI), or point mutual information, is a measure of association used in information theory and statistics.

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Poisson distribution

In probability theory and statistics, the Poisson distribution (in English often rendered), named after French mathematician Siméon Denis Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event.

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Poisson point process

In probability, statistics and related fields, a Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object that consists of points randomly located on a mathematical space.

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Poisson random measure

Let (E, \mathcal A, \mu) be some measure space with \sigma-finite measure \mu.

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Poly-Weibull distribution

In probability theory and statistics, the poly-Weibull distribution is a continuous probability distribution.

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Polynomial least squares

In mathematical statistics, polynomial least squares comprises a broad range of statistical methods for estimating an underlying polynomial that describes observations.

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Polytomous Rasch model

The polytomous Rasch model is generalization of the dichotomous Rasch model.

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Popoviciu's inequality on variances

In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ² of any bounded probability distribution.

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Posterior probability

In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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Prior-independent mechanism

A Prior-independent mechanism (PIM) is a mechanism in which the designer knows that the agents' valuations are drawn from some probability distribution, but does not know the distribution.

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Probabilistic design

Probabilistic design is a discipline within engineering design.

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Probabilistic method

The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object.

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Probabilistic metric space

A probabilistic metric space is a generalization of metric spaces where the distance has no longer values in non-negative real numbers, but in distribution functions.

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Probabilistic risk assessment

Probabilistic risk assessment (PRA) is a systematic and comprehensive methodology to evaluate risks associated with a complex engineered technological entity (such as an airliner or a nuclear power plant) or the effects of stressors on the environment (Probabilistic Environmental Risk Assessment - PERA) for example.

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Probabilistic soft logic

Probabilistic soft logic (PSL) is a SRL framework for collective, probabilistic reasoning in relational domains.

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Probability box

A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Probability distribution of extreme points of a Wiener stochastic process

In the mathematical theory of probability, the Wiener process, named after Norbert Wiener, is a stochastic process used in modeling various phenomena, including Brownian motion and fluctuations in financial markets.

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Probability integral transform

In statistics, the probability integral transform or transformation relates to the result that data values that are modelled as being random variables from any given continuous distribution can be converted to random variables having a standard uniform distribution.

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Probability mass function

In probability and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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Probability of error

In statistics, the term "error" arises in two ways.

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Probability of success

The probability of success (POS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making.

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Probability space

In probability theory, a probability space or a probability triple (\Omega, \mathcal, P) is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Probability vector

In mathematics and statistics, a probability vector or stochastic vector is a vector with non-negative entries that add up to one.

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Probability-generating function

In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable.

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Product (mathematics)

In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.

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Product distribution

A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions.

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Product integral

A "product integral" is any product-based counterpart of the usual sum-based integral of classical calculus.

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Pseudo-marginal Metropolis–Hastings algorithm

In computational statistics, the pseudo-marginal Metropolis–Hastings algorithm is a Monte Carlo method to sample from a probability distribution.

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Pseudolikelihood

In statistical theory, a pseudolikelihood is an approximation to the joint probability distribution of a collection of random variables.

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Q-Gaussian distribution

The q-Gaussian is a probability distribution arising from the maximization of the Tsallis entropy under appropriate constraints.

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Q-Weibull distribution

No description.

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Quadratic form (statistics)

In multivariate statistics, if \varepsilon is a vector of n random variables, and \Lambda is an n-dimensional symmetric matrix, then the scalar quantity \varepsilon^T\Lambda\varepsilon is known as a quadratic form in \varepsilon.

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Quantile

In statistics and probability quantiles are cut points dividing the range of a probability distribution into contiguous intervals with equal probabilities, or dividing the observations in a sample in the same way.

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Quantile function

In probability and statistics, the quantile function specifies, for a given probability in the probability distribution of a random variable, the value at which the probability of the random variable is less than or equal to the given probability.

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Quantization (signal processing)

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set.

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Quantum probability

Quantum probability was developed in the 1980s as a noncommutative analog of the Kolmogorovian theory of stochastic processes.

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Quantum statistical mechanics

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems.

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Radon–Nikodym theorem

In mathematics, the Radon–Nikodym theorem is a result in measure theory.

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Raikov's theorem

In probability theory, Raikov’s theorem, named after Dmitry Raikov, states that if the sum of two independent non-negative random variables X and Y has a Poisson distribution, then both X and Y themselves must have the Poisson distribution.

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Random (disambiguation)

Randomness is the property of lacking any sensible predictability.

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Random compact set

In mathematics, a random compact set is essentially a compact set-valued random variable.

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Random effects model

In statistics, a random effects model, also called a variance components model, is a statistical model where the model parameters are random variables.

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Random element

In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line.

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Random energy model

In statistical physics of disordered systems, the random energy model is a toy model of a system with quenched disorder.

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Random field

A random field is a generalization of a stochastic process such that the underlying parameter need no longer be a simple real or integer valued "time", but can instead take values that are multidimensional vectors, or points on some manifold.

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Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs.

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Random mapping

When the data vectors are high-dimensional it is computationally infeasible to use data analysis or pattern recognition algorithms which repeatedly compute similarities or distances in the original data space.

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Random matrix

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.

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Random measure

In probability theory, a random measure is a measure-valued random element.

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Random number generation

Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator (RNG).

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Random permutation

A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.

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Random sequence

The concept of a random sequence is essential in probability theory and statistics.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Random variate

In the mathematical fields of probability and statistics, a random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable might have different values.

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Random walk

A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.

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Random-sampling mechanism

A random-sampling mechanism (RSM) is a truthful mechanism that uses sampling in order to achieve approximately-optimal gain in prior-free mechanisms and prior-independent mechanisms.

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Randomized algorithm

A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.

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Randomness

Randomness is the lack of pattern or predictability in events.

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Randomness merger

In extractor theory, a randomness merger is a function which extracts randomness out of a set of random variables, provided that at least one of them is uniformly random.

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Rao–Blackwell theorem

In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria.

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Ratio distribution

A ratio distribution (or quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions.

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Rayleigh distribution

No description.

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Rayleigh fading

Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.

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Real estate in Puerto Rico

As of 2012, the real estate industry in Puerto Rico constituted about 14.8% of the gross domestic product of Puerto Rico, about 1% of all of the employee compensation on the island and, together with finance and insurance (FIRE), about 3.7% of all the employment on the jurisdiction.

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Real-valued function

In mathematics, a real-valued function is a function whose values are real numbers.

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Realization (probability)

In probability and statistics, a realization, observation, or observed value, of a random variable is the value that is actually observed (what actually happened).

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Rectified Gaussian distribution

In probability theory, the rectified Gaussian distribution is a modification of the Gaussian distribution when its negative elements are reset to 0 (analogous to an electronic rectifier).

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Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.

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Regression toward the mean

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first.

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Regular conditional probability

Regular conditional probability is a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions.

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Rejection sampling

In numerical analysis, rejection sampling is a basic technique used to generate observations from a distribution.

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Rencontres numbers

In combinatorial mathematics, the rencontres numbers are a triangular array of integers that enumerate permutations of the set with specified numbers of fixed points: in other words, partial derangements.

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Renewal theory

Renewal theory is the branch of probability theory that generalizes Poisson processes for arbitrary holding times.

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Residence time (statistics)

In statistics, the residence time is the average amount of time it takes for a random process to reach a certain boundary value, usually a boundary far from the mean.

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Response modeling methodology

Response modeling methodology (RMM) is a general platform for modeling monotonic convex relationships.

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Revenue equivalence

Revenue equivalence is a concept in auction theory that states that given certain conditions, any mechanism that results in the same outcomes (i.e. allocates items to the same bidders) also has the same expected revenue.

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Riemann–Stieltjes integral

In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.

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Risk factor (finance)

A risk factor is a concept in finance theory such as the CAPM, arbitrage pricing theory and other theories that use pricing kernels.

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Risk-neutral measure

In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.

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Robbins lemma

In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and f is any function for which the expected value E(f(X)) exists, then Robbins introduced this proposition while developing empirical Bayes methods.

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Robbins' problem

In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information.

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Rule of succession

In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem.

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Runge–Kutta method (SDE)

In mathematics of stochastic systems, the Runge–Kutta method is a technique for the approximate numerical solution of a stochastic differential equation.

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RV (disambiguation)

An RV is a recreational vehicle, a motorhome.

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RV coefficient

In statistics, the RV coefficient is a multivariate generalization of the squared Pearson correlation coefficient (because the RV coefficient takes values between 0 and 1).

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Sample mean and covariance

The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.

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Sampling distribution

In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.

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Scale invariance

In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, thus represent a universality.

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Scheffé’s lemma

In mathematics, Scheffé's lemma is a proposition in measure theory concerning the convergence of sequences of integrals.

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Schrödinger method

In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of distribution and occupancy.

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Schuette–Nesbitt formula

In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle.

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Scoring algorithm

Scoring algorithm, also known as Fisher's scoring, is a form of Newton's method used in statistics to solve maximum likelihood equations numerically, named after Ronald Fisher.

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Second moment method

In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive.

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Secretary problem

The secretary problem is a famous problem that demonstrates a scenario involving the optimal stopping theory.

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Self-information

In information theory, self-information or surprisal is the surprise when a random variable is sampled.

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Self-similar process

Self-similar processes are types of stochastic processes that exhibit the phenomenon of self-similarity.

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Sergei Natanovich Bernstein

Sergei Natanovich Bernstein (Серге́й Ната́нович Бернште́йн, sometimes Romanized as Bernshtein; 5 March 1880 – 26 October 1968) was a Russian and Soviet mathematician of Jewish origin known for contributions to partial differential equations, differential geometry, probability theory, and approximation theory.

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Set function

In mathematics, a set function is a function whose input is a set.

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Set-theoretic limit

In mathematics, the '''limit''' of a sequence of sets A1, A2,...

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Seven states of randomness

The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution.

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Sexual dimorphism measures

Although the subject of sexual dimorphism is not in itself controversial, the measures by which it is assessed differ widely.

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Shannon's source coding theorem

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy.

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Shearer's inequality

In information theory, Shearer's inequality, named after James Shearer, states that if X1,..., Xd are random variables and S1,..., Sn are subsets of such that every integer between 1 and d lies in at least r of these subsets, then where (X_)_ is the Cartesian product of random variables X_ with indices j in S_ (so the dimension of this vector is equal to the size of S_).

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Shifted Gompertz distribution

No description.

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Sigma

Sigma (upper-case Σ, lower-case σ, lower-case in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet.

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Sigma-algebra

In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under countable unions and countable intersections.

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Sign test

The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment.

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Signal-to-interference-plus-noise ratio

In information theory and telecommunication engineering, the signal-to-interference-plus-noise ratio (SINR) (also known as the signal-to-noise-plus-interference ratio (SNIR)) is a quantity used to give theoretical upper bounds on channel capacity (or the rate of information transfer) in wireless communication systems such as networks.

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Singular function

In mathematics, a real-valued function f on the interval is said to be singular if it has the following properties.

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Skellam distribution

The Skellam distribution is the discrete probability distribution of the difference N_1-N_2 of two statistically independent random variables N_1 and N_2, each Poisson-distributed with respective expected values \mu_1 and \mu_2 It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in sports where all scored points are equal, such as baseball, hockey and soccer.

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Skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

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Skorokhod integral

In mathematics, the Skorokhod integral, often denoted δ, is an operator of great importance in the theory of stochastic processes.

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Skorokhod's embedding theorem

In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard any suitable collection of random variables as a Wiener process (Brownian motion) evaluated at a collection of stopping times.

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Skorokhod's representation theorem

In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of probability measures whose limit measure is sufficiently well-behaved can be represented as the distribution/law of a pointwise convergent sequence of random variables defined on a common probability space.

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Slash distribution

In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate.

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Slice sampling

Slice sampling is a type of Markov chain Monte Carlo algorithm for pseudo-random number sampling, i.e. for drawing random samples from a statistical distribution.

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Slope stability analysis

Slope stability analysis is performed to assess the safe design of a human-made or natural slopes (e.g. embankments, road cuts, open-pit mining, excavations, landfills etc.) and the equilibrium conditions.

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Slutsky's theorem

In probability theory, Slutsky’s theorem extends some properties of algebraic operations on convergent sequences of real numbers to sequences of random variables.

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Smoothness (probability theory)

In probability theory and statistics, smoothness of a density function is a measure which determines how many times the density function can be differentiated, or equivalently the limiting behavior of distribution’s characteristic function.

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Spatial dependence

Spatial dependence is the spatial relationship of variable values (for themes defined over space, such as rainfall) or locations (for themes defined as objects, such as cities).

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Square (algebra)

In mathematics, a square is the result of multiplying a number by itself.

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Squared deviations from the mean

Squared deviations from the mean (SDM) are involved in various calculations.

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Squashed entanglement

Squashed entanglement, also called CMI entanglement (CMI can be pronounced "see me"), is an information theoretic measure of quantum entanglement for a bipartite quantum system.

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St. Petersburg paradox

The St.

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Stability (probability)

In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters.

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Stability postulate

In probability theory, to obtain a nondegenerate limiting distribution of the extreme value distribution, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size.

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Stable distribution

No description.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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Standard normal deviate

A standard normal deviate (or standard normal variable) is a normally distributed random variable with expected value 0 and variance 1.

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Standard score

In statistics, the standard score is the signed number of standard deviations by which the value of an observation or data point differs from the mean value of what is being observed or measured.

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Standardized moment

In probability theory and statistics, the standardized moment of a probability distribution is a moment (normally a higher degree central moment) that is normalized.

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Standardized mortality ratio

In epidemiology, the standardized mortality ratio or SMR, is a quantity, expressed as either a ratio or percentage quantifying the increase or decrease in mortality of a study cohort with respect to the general population.

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Stationary process

In mathematics and statistics, a stationary process (a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.

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Stationary sequence

In probability theory – specifically in the theory of stochastic processes, a stationary sequence is a random sequence whose joint probability distribution is invariant over time.

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Statistic

A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value).

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Statistical association football predictions

Statistical Football prediction is a method used in sports betting, to predict the outcome of football matches by means of statistical tools.

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Statistical data type

In statistics, groups of individual data points may be classified as belonging to any of various statistical data types, e.g. categorical ("red", "blue", "green"), real number (1.68, -5, 1.7e+6),odd number(1,3,5) etc.

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Statistical dispersion

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

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Statistical distance

In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.

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Statistical hypothesis testing

A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.

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Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population.

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Statistical parameter

A statistical parameter or population parameter is a quantity that indexes a family of probability distributions.

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Statistical unit

A unit in a statistical analysis is one member of a set of entities being studied.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Stein's example

Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately.

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Stein's lemma

Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference — in particular, to James–Stein estimation and empirical Bayes methods — and its applications to portfolio choice theory.

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Stein's method

Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric.

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Stern–Gerlach experiment

The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized.

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Stirling numbers of the second kind

In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by S(n,k) or \textstyle \lbrace\rbrace.

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Stochastic approximation

Stochastic approximation algorithms are recursive update rules that can be used, among other things, to solve optimization problems and fixed point equations (including standard linear systems) when the collected data is subject to noise.

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Stochastic discount factor

The stochastic discount factor (SDF) is a concept in financial economics and mathematical finance.

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Stochastic dominance

Stochastic dominance is a partial order between random variables.

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Stochastic dynamic programming

Originally introduced by Richard E. Bellman in, stochastic dynamic programming is a technique for modelling and solving problems of decision making under uncertainty.

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Stochastic equicontinuity

In estimation theory in statistics, stochastic equicontinuity is a property of estimators (estimation procedures) that is useful in dealing with their asymptotic behaviour as the amount of data increases.

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Stochastic geometry models of wireless networks

In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks.

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Stochastic homogenization

In homogenization theory, a branch of mathematics, stochastic homogenization is a technique for understanding solutions to partial differential equations with oscillatory random coefficients.

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Stochastic matrix

In mathematics, a stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix) is a square matrix used to describe the transitions of a Markov chain.

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Stochastic modelling (insurance)

"Stochastic" means being or having a random variable.

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Stochastic optimization

Stochastic optimization (SO) methods are optimization methods that generate and use random variables.

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Stochastic ordering

In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another.

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Stochastic Petri net

Stochastic Petri nets are a form of Petri net where the transitions fire after a probabilistic delay determined by a random variable.

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Stochastic process

--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.

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Stochastic programming

In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty.

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Stopping time

In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time) is a specific type of “random time”: a random variable whose value is interpreted as the time at which a given stochastic process exhibits a certain behavior of interest.

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Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

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Studentized range

In statistics, the studentized range is the difference between the largest and smallest data in a sample measured in units of sample standard deviations, so long as the standard deviation used is independent of the data.

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Subindependence

In probability theory and statistics, subindependence is a weak form of independence.

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Submodular set function

In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases.

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Sum of normally distributed random variables

In probability theory, calculation of the sum of normally distributed random variables is an instance of the arithmetic of random variables, which can be quite complex based on the probability distributions of the random variables involved and their relationships.

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Sunspots (economics)

In economics, the term sunspots (or sometimes "a sunspot") usually refers to an extrinsic random variable, that is, a random variable that does not affect economic fundamentals (such as endowments, preferences, or technology).

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Survival analysis

Survival analysis is a branch of statistics for analyzing the expected duration of time until one or more events happen, such as death in biological organisms and failure in mechanical systems.

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Survival function

The survival function is a function that gives the probability that a patient, device, or other object of interest will survive beyond any given specified time.

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Symmetric probability distribution

In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged when its probability density function or probability mass function is reflected around a vertical line at some value of the random variable represented by the distribution.

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System size expansion

The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampenvan Kampen, N. G. (2007) "Stochastic Processes in Physics and Chemistry", North-Holland Personal Library used in the analysis of stochastic processes.

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Taguchi methods

Taguchi methods (タグチメソッド) are statistical methods, or sometimes called robust design methods, developed by Genichi Taguchi to improve the quality of manufactured goods, and more recently also applied to engineering, biotechnology, marketing and advertising.

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Tail dependence

In probability theory, the tail dependence of a pair of random variables is a measure of their comovements in the tails of the distributions.

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Tail value at risk

Tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk.

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Taylor expansions for the moments of functions of random variables

In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Telescoping series

In mathematics, a telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation.

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The Correlation between Relatives on the Supposition of Mendelian Inheritance

"The Correlation between Relatives on the Supposition of Mendelian Inheritance" is a scientific paper by Ronald Fisher which was published in the Philosophical Transactions of the Royal Society of Edinburgh in 1918, (volume 52, pages 399–433).

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Theoretical ecology

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis.

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Threshold model

In mathematical or statistical modeling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model varies in some important way.

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Tightness of measures

In mathematics, tightness is a concept in measure theory.

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Tilde

The tilde (in the American Heritage dictionary or; ˜ or ~) is a grapheme with several uses.

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Total correlation

In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information.

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Touchard polynomials

The Touchard polynomials, studied by, also called the exponential polynomials or Bell polynomials, comprise a polynomial sequence of binomial type defined by \left\x^k, where S(n,k).

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Treap

In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys.

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Tweedie distribution

In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal and gamma distributions, the purely discrete scaled Poisson distribution, and the class of mixed compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous.

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Twelvefold way

In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.

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Twisting properties

Starting with a sample \ observed from a random variable X having a given distribution law with a non-set parameter, a parametric inference problem consists of computing suitable values – call them estimates – of this parameter precisely on the basis of the sample.

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Two-moment decision model

In decision theory, economics, and finance, a two-moment decision model is a model that describes or prescribes the process of making decisions in a context in which the decision-maker is faced with random variables whose realizations cannot be known in advance, and in which choices are made based on knowledge of two moments of those random variables.

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Two-way analysis of variance

In statistics, the two-way analysis of variance (ANOVA) is an extension of the one-way ANOVA that examines the influence of two different categorical independent variables on one continuous dependent variable.

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Unbiased estimation of standard deviation

In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.

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Uncertainty

Uncertainty has been called "an unintelligible expression without a straightforward description".

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Uncorrelated random variables

In probability theory and statistics, two real-valued random variables, X,Y, are said to be uncorrelated if their covariance, E(XY) − E(X)E(Y), is zero.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Uniform integrability

In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the theory of martingales.

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Univariate distribution

In statistics, a univariate distribution is a probability distribution of only one random variable.

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Up tack

The up tack or falsum (⊥, \bot in LaTeX, U+22A5 in Unicode) is a constant symbol used to represent.

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Urn problem

In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container.

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Ursell function

In statistical mechanics, an Ursell function or connected correlation function, is a cumulant of a random variable.

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Value of control

The value of control is a quantitative measure of the value of controlling the outcome of an uncertain variable.

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Van der Corput inequality

In mathematics, the van der Corput inequality is a corollary of the Cauchy–Schwarz inequality that is useful in the study of correlations among vectors, and hence random variables.

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Van Houtum distribution

In probability theory and statistics, the Van Houtum distribution is a discrete probability distribution named after prof.

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Varadhan's lemma

In mathematics, Varadhan's lemma is a result from large deviations theory named after S. R. Srinivasa Varadhan.

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Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

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Variable-order Markov model

In stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models.

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Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

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Variance-gamma distribution

The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution.

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Variational Bayesian methods

Variational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning.

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Vector (mathematics and physics)

When used without any further description, vector usually refers either to.

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Viral phylodynamics

Viral phylodynamics is defined as the study of how epidemiological, immunological, and evolutionary processes act and potentially interact to shape viral phylogenies.

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Vivek Borkar

Vivek Shripad Borkar (born 1954) is an Indian electrical engineer, mathematician and an Institute chair professor at the Indian Institute of Technology, Mumbai.

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Vysochanskij–Petunin inequality

In probability theory, the Vysochanskij–Petunin inequality gives a lower bound for the probability that a random variable with finite variance lies within a certain number of standard deviations of the variable's mean, or equivalently an upper bound for the probability that it lies further away.

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Wald–Wolfowitz runs test

The Wald–Wolfowitz runs test (or simply runs test), named after Abraham Wald and Jacob Wolfowitz, both of whom are well known staticians.

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Wallenius' noncentral hypergeometric distribution

In probability theory and statistics, Wallenius' noncentral hypergeometric distribution (named after Kenneth Ted Wallenius) is a generalization of the hypergeometric distribution where items are sampled with bias.

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Wasserstein metric

In mathematics, the Wasserstein or Kantorovich-Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on M, the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved.

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Wassily Hoeffding

Wassily Hoeffding (June 12, 1914 – February 28, 1991) was a Finnish statistician and probabilist.

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Weakly dependent random variables

In probability, weakly dependence of random variables is a generalization of independence that is weaker than the concept of a martingale.

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Weakly measurable function

In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense.

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Weibull distribution

No description.

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White noise

In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.

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Whitening transformation

A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1.

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Wick product

In probability theory, the Wick product is a particular way of defining an adjusted product of a set of random variables.

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Wiener sausage

In the mathematical field of probability, the Wiener sausage is a neighborhood of the trace of a Brownian motion up to a time t, given by taking all points within a fixed distance of Brownian motion.

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Wishart distribution

In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution.

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Witch of Agnesi

In mathematics, the Witch of Agnesi is a cubic plane curve defined from two diametrically opposite points of a circle.

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Workplace respirator testing

To protect workers from air contaminants employers often used respirators.

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Xi (letter)

Xi (uppercase Ξ, lowercase ξ; ξι) is the 14th letter of the Greek alphabet.

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X̅ and R chart

In statistical quality control, the \bar x and R chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process.

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X̅ and s chart

In statistical quality control, the \bar x and s chart is a type of control chart used to monitor variables data when samples are collected at regular intervals from a business or industrial process.

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Z-channel (information theory)

A Z-channel is a communications channel used in coding theory and information theory to model the behaviour of some data storage systems.

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Zero-truncated Poisson distribution

In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers.

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Zeta distribution

In probability theory and statistics, the zeta distribution is a discrete probability distribution.

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(a,b,0) class of distributions

In probability theory, the distribution of a discrete random variable N whose values are nonnegative integers is said to be a member of the (a, b, 0) class of distributions if its probability mass function obeys where p_k.

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18XX

18XX is the generic term for a series of board games that, with a few exceptions, recreate the building of railroad corporations during the 19th century; individual games within the series use particular years in the 19th century as their title (usually the date of the start of railway development in the area of the world they cover), or "18" plus a two-letter geographical designator (such as 18EU for a game set in the European Union).

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1937 in science

The year 1937 in science and technology involved some significant events, listed below.

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68–95–99.7 rule

In statistics, the 68–95–99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

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Aleatory variable, Discrete random variable, Equal in distribution, Random Variable, Random variables, Random variation, RandomVariable, Statistical variable, Stochastic variable.

References

[1] https://en.wikipedia.org/wiki/Random_variable

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