the generalized beta distribution is a continuous probability distribution with four shape parameters, including more than thirty named distributions as...

The symmetric generalized normal distribution, also known as the exponential power distribution or the generalized error distribution, is a parametric...

probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1)...

parameter. Both are in turn special cases of the even more general generalized beta distribution of the second kind. Another more straightforward generalization...

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing...

statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or...

probability theory and statistics, the beta prime distribution (also known as inverted beta distribution or beta distribution of the second kind) is an absolutely...

The generalized gamma distribution is a continuous probability distribution with two shape parameters (and a scale parameter). It is a generalization...

{\displaystyle \beta =1/\theta } ⁠, called a rate parameter. In each of these forms, both parameters are positive real numbers. The distribution has important...

In statistics, the generalized Dirichlet distribution (GD) is a generalization of the Dirichlet distribution with a more general covariance structure...

The term generalized logistic distribution is used as the name for several different families of probability distributions. For example, Johnson et al...

bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the beta distribution, but much...

multinomial distribution, a generalization of the beta negative binomial distribution. The generalized multivariate log-gamma distribution The Marshall–Olkin...

In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another...

theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value...

κ-exponential distribution in the κ = 0 {\displaystyle \kappa =0} case. Exponential distribution is a limit of the κ-Generalized Gamma distribution in the α...

additive model Generalized additive model for location, scale and shape Generalized beta distribution Generalized canonical correlation Generalized chi-squared...

and statistics, the skewed generalized "t" distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis...

probability theory and statistics, the beta-binomial distribution is a family of discrete probability distributions on a finite support of non-negative integers...

statistics, the generalized inverse Gaussian distribution (GIG) is a three-parameter family of continuous probability distributions with probability...

In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable  X {\displaystyle X} equal...

distributions parameterized by a vector α {\displaystyle {\boldsymbol {\alpha }}} of positive reals. It is a multivariate generalization of the beta distribution...

e − ( β x ) k {\displaystyle f(x;k,\beta )=\beta k({\beta x})^{k-1}e^{-(\beta x)^{k}}} the cumulative distribution function is F ( x ; k , β ) = 1 − e...

follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax...

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth...

distribution and normal distribution. (See the previous section.) The Pareto distribution is a special case of the generalized Pareto distribution, which is a family...

{\displaystyle X_{i}} follows the generalized normal distribution (version 1) with parameters μ , α , β {\displaystyle \mu ,\alpha ,\beta } then ∑ i = 1 n 2 | X...

{\sqrt {x(1-x)}}}}} on (0, 1). The standard arcsine distribution is a special case of the beta distribution with α = β = 1/2. That is, if X {\displaystyle...

β , {\displaystyle \beta ,} the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of k {\displaystyle...

{\Sigma }}} , also known as the generalized variance. The equation above reduces to that of the univariate normal distribution if Σ {\displaystyle {\boldsymbol...