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Generalized integer gamma distribution information


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. This is a special case of the generalized chi-squared distribution. A related concept is the generalized near-integer gamma distribution (GNIG).

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Generalized gamma distribution

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

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Generalized integer gamma distribution

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the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape...

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Gamma distribution

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The gamma distribution is a special case of the generalized gamma distribution, the generalized integer gamma distribution, and the generalized inverse...

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Generalized normal distribution

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

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Gamma function

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complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Γ ( n ) = ( n − 1...

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Gumbel distribution

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

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Negative binomial distribution

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distribution on the set of all nonnegative integers.) Now we also allow non-integer values of r. Then we have a proper negative binomial distribution...

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Generalized linear model

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

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Erlang distribution

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{\displaystyle k=1} , the distribution simplifies to the exponential distribution. The Erlang distribution is a special case of the gamma distribution in which the...

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Poisson distribution

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Binomial distribution Compound Poisson distribution Conway–Maxwell–Poisson distribution Erlang distribution Exponential distribution Gamma distribution Hermite...

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Weibull distribution

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. A Weibull distribution is a generalized gamma distribution with both shape parameters equal to k. The translated Weibull distribution (or 3-parameter...

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Generalized Pareto distribution

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

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Normal distribution

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expressions remain valid even if p {\displaystyle p} is not an integer. See also generalized Hermite polynomials. The expectation of X {\displaystyle X}...

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Exponential distribution

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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...

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List of probability distributions

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inverse-gamma distribution The generalized gamma distribution The generalized Pareto distribution The Gamma/Gompertz distribution The Gompertz distribution The...

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Pareto distribution

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

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Beta distribution

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chi-squared distribution X ~ χ2(k) is a special case of the gamma distribution, with parametrization X ~ Γ(k/2, 1/2) where k is a positive integer that specifies...

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Incomplete gamma function

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the singularities of γ ( s , z ) {\displaystyle \gamma (s,z)} (at z = 0 or s a non-positive integer), whereas the last factor contributes to its zeros...

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Dirichlet distribution

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)={\frac {\Gamma (\alpha K)}{\Gamma (\alpha )^{K}}}\prod _{i=1}^{K}x_{i}^{\alpha -1}.} When α=1[1], the symmetric Dirichlet distribution is equivalent...

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Tweedie distribution

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Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the...

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Beta negative binomial distribution

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Markov-Pólya distribution and the generalized Waring distribution or simply abbreviated as the BNB distribution. A shifted form of the distribution has been...

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Multinomial distribution

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}}\end{cases}}\end{aligned}}} for non-negative integers x1, ..., xk. The probability mass function can be expressed using the gamma function as: f ( x 1 , … , x k ;...

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Wishart distribution

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In statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart, who...

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Cumulative distribution function

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{\displaystyle F_{X}} to be constant). In this case, one may use the generalized inverse distribution function, which is defined as F − 1 ( p ) = inf { x ∈ R : F...

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Kaniadakis Gamma distribution

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Kaniadakis Generalized Gamma distribution (or κ-Generalized Gamma distribution) is a four-parameter family of continuous statistical distributions, supported...

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Chi distribution

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to a chi distribution with k {\displaystyle k} degrees of freedom chi distribution is a special case of the generalized gamma distribution or the Nakagami...

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