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

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

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

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

Scaled inverse chi-squared distribution Gamma distribution Generalized chi-squared distribution Noncentral chi-squared distribution Pearson's chi-squared test...

n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer ⁠ n {\displaystyle n} ⁠. The gamma function can be defined via a convergent...

(2-dimensional). The Poisson distribution is an appropriate model if the following assumptions are true: k, a nonnegative integer, is the number of times an...

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

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

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

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

Elias γ {\displaystyle \gamma } code or Elias gamma code is a universal code encoding positive integers developed by Peter Elias.: 197, 199  It is used...

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

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...

gamma–Poisson (mixture) distribution. The negative binomial distribution was originally derived as a limiting case of the gamma-Poisson distribution....

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

Student's t distribution (or simply the t distribution) t ν {\displaystyle t_{\nu }} is a continuous probability distribution that generalizes the standard...

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

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

The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined...

proofs of this without using the generalized Riemann hypothesis. In 1917, Hardy and Littlewood showed that the generalized Riemann hypothesis implies a conjecture...

Yule–Simon (ρ) distribution is f ( k ; ρ ) = ρ B ⁡ ( k , ρ + 1 ) , {\displaystyle f(k;\rho )=\rho \operatorname {B} (k,\rho +1),} for integer k ≥ 1 {\displaystyle...

independent gamma variates. If instead one normalizes generalized gamma variates, one obtains variates from the simplicial generalized beta distribution (SGB)...

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

= 1 N R i 2 {\displaystyle \sum _{i=1}^{N}R_{i}^{2}} has a gamma distribution with integer scale parameter N {\displaystyle N} and rate parameter 1 2...

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

Distributions, also known as Schwartz distributions are a kind of generalized function in mathematical analysis. Distributions make it possible to differentiate...

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...

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...

binomial coefficients can be generalized to ( z k ) {\displaystyle {\tbinom {z}{k}}} for any complex number z and integer k ≥ 0, and many of their properties...