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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. 

58 relations: Almost everywhere, Antithetic variates, Bates distribution, Bernoulli number, Beta distribution, Bias of an estimator, Bit numbering, Borel set, Box–Muller transform, Central moment, Cumulant, Cumulative distribution function, Discrete uniform distribution, Efficiency (statistics), Expected value, Exponential distribution, Fourier analysis, German tank problem, Heaviside step function, Independent and identically distributed random variables, Integral transform, Interval (mathematics), Inverse transform sampling, Irwin–Hall distribution, Journal of Econometrics, Lebesgue measure, Maximum entropy probability distribution, Maximum likelihood estimation, Maximum spacing estimation, Measure (mathematics), Method of moments (statistics), Mid-range, Minimum-variance unbiased estimator, Moment (mathematics), Moment-generating function, Normal distribution, Null hypothesis, Order statistic, P-value, Probability density function, Probability distribution, Probability plot, Probability theory, Programming language, Pseudorandom number generator, Q–Q plot, Random variable, Rectangular function, Rejection sampling, Root-mean-square deviation, ... Expand index (8 more) »

## Almost everywhere

In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities.

## Antithetic variates

In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods.

## Bates distribution

In probability and statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval.

## Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.

## 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.

## Bias of an estimator

In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated.

## Bit numbering

In computing, bit numbering (or sometimes bit endianness) is the convention used to identify the bit positions in a binary number or a container for such a value.

## Borel set

In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement.

## Box–Muller transform

The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a pseudo-random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers.

## 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.

## 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.

## 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.

## Discrete uniform distribution

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.

## Efficiency (statistics)

In the comparison of various statistical procedures, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure.

## 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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## Fourier analysis

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

## German tank problem

In the statistical theory of estimation, the German tank problem consists in estimating the maximum of a discrete uniform distribution from sampling without replacement.

## 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.

## 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.

## Integral transform

In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.

## Interval (mathematics)

In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.

## 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.

## 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.

## Journal of Econometrics

The Journal of Econometrics is a scholarly journal in econometrics.

## Lebesgue measure

In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.

## 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.

## Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

## Maximum spacing estimation

In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model.

## Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

## Method of moments (statistics)

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

## Mid-range

In statistics, the mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as: The mid-range is the midpoint of the range; as such, it is a measure of central tendency.

## Minimum-variance unbiased estimator

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.

## 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.

## 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.

## Normal distribution

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

## Null hypothesis

In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.

## Order statistic

In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value.

## 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.

## 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.

## 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.

## Probability plot

In statistics, a probability plot is a graphical technique for comparing two data sets, either two sets of empirical observations, one empirical set against a theoretical set, or (more rarely) two theoretical sets against each other.

## Probability theory

Probability theory is the branch of mathematics concerned with probability.

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

## Pseudorandom number generator

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers.

## Q–Q plot

In statistics, a Q–Q (quantile-quantile) plot is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantiles against each other.

## 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.

## Rectangular function

The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as: 0 & \mbox |t| > \frac \\ \frac & \mbox |t|.

## Rejection sampling

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

## Root-mean-square deviation

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) (or sometimes root-mean-squared error) is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed.

## Sample maximum and minimum

In statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample.

## Sample size determination

Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample.

## Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

## Statistics

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

## Symmetric probability distribution

In statistics, a symmetric probability distribution is a probability distribution&mdash;an assignment of probabilities to possible occurrences&mdash;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.

## Triangular distribution

In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b and mode c, where a \left.\begin f(x) &.

## Variance

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

## World War II

World War II (often abbreviated to WWII or WW2), also known as the Second World War, was a global war that lasted from 1939 to 1945, although conflicts reflecting the ideological clash between what would become the Allied and Axis blocs began earlier.

## References

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