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Symmetric probability distribution

Index 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. [1]

38 relations: Arcsine distribution, Bates distribution, Cauchy distribution, Central moment, Champernowne distribution, Degenerate distribution, Discrete uniform distribution, Elliptical distribution, Gaussian q-distribution, Generalized normal distribution, Hyperbolic secant distribution, If and only if, Irwin–Hall distribution, Laplace distribution, Logistic distribution, Mean, Median, Mode (statistics), Normal distribution, Normal-exponential-gamma distribution, Probability density function, Probability distribution, Probability mass function, Rademacher distribution, Raised cosine distribution, Random variable, Reflection (mathematics), Skewness, Statistics, Student's t-distribution, Symmetry in mathematics, Tukey lambda distribution, U-quadratic distribution, Uniform distribution (continuous), Unimodality, Voigt profile, Von Mises distribution, Wigner semicircle distribution.

Arcsine distribution

In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function is for 0 ≤ x ≤ 1, and whose probability density function is on (0, 1).

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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.

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Cauchy distribution

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

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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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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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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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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.

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Elliptical distribution

In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution.

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Gaussian q-distribution

In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution.

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Generalized normal distribution

The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line.

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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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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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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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Laplace distribution

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

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Logistic distribution

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

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Mean

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

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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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Mode (statistics)

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

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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-exponential-gamma distribution

In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions.

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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 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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Rademacher distribution

No description.

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Raised cosine distribution

In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval.

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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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Reflection (mathematics)

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection.

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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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Statistics

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

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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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Symmetry in mathematics

Symmetry occurs not only in geometry, but also in other branches of mathematics.

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Tukey lambda distribution

Formalized by John Tukey, the Tukey lambda distribution is a continuous, symmetric probability distribution defined in terms of its quantile function.

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U-quadratic distribution

In probability theory and statistics, the U-quadratic distribution is a continuous probability distribution defined by a unique convex quadratic function with lower limit a and upper limit b.

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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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Unimodality

In mathematics, unimodality means possessing a unique mode.

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Voigt profile

In spectroscopy, the Voigt profile (named after Woldemar Voigt) is a line profile resulting from the convolution of two broadening mechanisms, one of which alone would produce a Gaussian profile (usually, as a result of the Doppler broadening), and the other would produce a Lorentzian profile.

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Von Mises distribution

In probability theory and directional statistics, the von Mises distribution (also known as the circular normal distribution or Tikhonov distribution) is a continuous probability distribution on the circle.

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Wigner semicircle distribution

The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse): for −R ≤ x ≤ R, and f(x).

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References

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

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