the gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and...

inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the...

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

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

exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. The...

{\displaystyle f(x;x_{0},\gamma )} is the distribution of the x-intercept of a ray issuing from ( x 0 , γ ) {\displaystyle (x_{0},\gamma )} with a uniformly...

{\displaystyle \gamma _{2}={\frac {-6\Gamma _{1}^{4}+12\Gamma _{1}^{2}\Gamma _{2}-3\Gamma _{2}^{2}-4\Gamma _{1}\Gamma _{3}+\Gamma _{4}}{[\Gamma _{2}-\Gamma _{1}^{2}]^{2}}}}...

chi-squared distribution χ k 2 {\displaystyle \chi _{k}^{2}} is a special case of the gamma distribution and the univariate Wishart distribution. Specifically...

normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is...

inverse gamma distribution is the conjugate prior distribution of the variance of a Gaussian distribution. As a result, the location-scale t distribution arises...

Gamma (/ˈɡæmə/ ; uppercase Γ, lowercase γ; Greek: γάμμα, romanized: gámma) is the third letter of the Greek alphabet. In the system of Greek numerals...

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

)={\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...

that the product of two independent Gamma-distributed samples (~Gamma(α,1) and Gamma(β,1)) has a K-distribution: f ( z , α , β ) = 2 Γ ( α ) − 1 Γ (...

generate random variates with compound gamma, or beta prime distributions. Another is via the ratio of independent gamma variates, as shown below. If X ∼ β...

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

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

the mean, and a vague prior probability (such as an exponential or gamma distribution) over the positive reals for the sample size, if they are independent...

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

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

{\displaystyle W=\mu +\sigma (Y^{-1}-1)^{\gamma },\qquad \sigma >0,\gamma >0,} then W has a Feller–Pareto distribution FP(μ, σ, γ, γ1, γ2). If U 1 ∼ Γ ( δ 1...

the normal-gamma distribution (or Gaussian-gamma distribution) is a bivariate four-parameter family of continuous probability distributions. It is the...

distribution Chi-square distribution Chow test Gamma distribution Hotelling's T-squared distribution Wilks' lambda distribution Wishart distribution Modified half-normal...

then ∑ i = 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...

Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. The family of Nakagami distributions has...

to the generalized multivariate log-gamma distribution provides a multivariate version of the Gumbel distribution. Gumbel has shown that the maximum value...

yields a Lomax distribution. Compounding a gamma distribution with inverse scale parameter distributed according to another gamma distribution yields a three-parameter...

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

M(t)={\frac {\Gamma (\alpha -t)\Gamma (\alpha +t)}{(\Gamma (\alpha ))^{2}}},\quad -\alpha <t<\alpha .} The corresponding cumulative distribution function is:...

Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution. A random variable has a Laplace ⁡ (...