# Category: Exponential family distributions

Complex Wishart distribution
In statistics, the complex Wishart distribution is a complex version of the Wishart distribution. It is the distribution of times the sample Hermitian covariance matrix of zero-mean independent Gaussi
Grouped Dirichlet distribution
In statistics, the grouped Dirichlet distribution (GDD) is a multivariate generalization of the Dirichlet distribution It was first described by Ng et al. 2008. The Grouped Dirichlet distribution aris
Inverse-Wishart distribution
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices. In Bayesian statistics
Beta distribution
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] in terms of two positive parameters, denoted by alpha (α)
Dirichlet distribution
In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted , is a family of continuous multivariate probability distributions parameterized by a ve
Gamma distribution
In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-square distri
Generalized inverse Gaussian distribution
In probability theory and statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability density function where Kp
Inverse-gamma distribution
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the recip
Exponential distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuo
Marshall–Olkin exponential distribution
In applied statistics, the Marshall–Olkin exponential distribution is any member of a certain family of continuous multivariate probability distributions with positive-valued components. It was introd
Complex inverse Wishart distribution
The complex inverse Wishart distribution is a matrix probability distribution defined on complex-valued positive-definite matrices and is the complex analog of the real inverse Wishart distribution. T
Weibull distribution
In probability theory and statistics, the Weibull distribution /ˈwaɪbʊl/ is a continuous probability distribution. It is named after Swedish mathematician Waloddi Weibull, who described it in detail i
Multivariate normal distribution
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) nor
Laplace distribution
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distributio
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,∞). Its probability
Zero degrees of freedom
In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). Thi
Pareto distribution
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto (Italian: [paˈreːto] US: /pəˈreɪtoʊ/ pə-RAY-toh), is a power-law probability distribution th
Scaled inverse chi-squared distribution
The scaled inverse chi-squared distribution is the distribution for x = 1/s2, where s2 is a sample mean of the squares of ν independent normal random variables that have mean 0 and inverse variance 1/
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. Just as the Laplace dist
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 c
Von Mises–Fisher distribution
In directional statistics, the von Mises–Fisher distribution (named after Richard von Mises and Ronald Fisher), is a probability distribution on the -sphere in . If the distribution reduces to the von
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. Thus, if the random variable X is
Inverted Dirichlet distribution
In statistics, the inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first described by Tiao and Cut
Generalized Dirichlet distribution
In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure and almost twice the number of parameters. Random
Continuous Bernoulli distribution
In probability theory, statistics, and machine learning, the continuous Bernoulli distribution is a family of continuous probability distributions parameterized by a single shape parameter , defined o
Rayleigh distribution
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distributio
Multinomial distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided dice rolled n times. F
Chi distribution
In probability theory and statistics, the chi distribution is a continuous probability distribution. It is the distribution of the positive square root of the sum of squares of a set of independent ra
Normal distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function i
Negative binomial distribution
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distribu
Geometric distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number X of Bernoulli trials needed to
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,
Inverse-chi-squared distribution
In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. It is closely r
Erlang distribution
The Erlang distribution is a two-parameter family of continuous probability distributions with support . The two parameters are: * a positive integer the "shape", and * a positive real number the "r
Wishart distribution
In statistics, the Wishart distribution is a generalization to multiple dimensions of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. It is
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
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