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In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. [1] The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. [2] There are two equivalent parameterizations in common use:
If X 1 and X 2 are Poisson random variables with means μ 1 and μ 2 respectively, then X 1 + X 2 is a Poisson random variable with mean μ 1 + μ 2. The sum of gamma (α i, β) random variables has a gamma (Σα i, β) distribution. If X 1 is a Cauchy (μ 1, σ 1) random variable and X 2 is a Cauchy (μ 2, σ 2), then X 1 + X 2 is a Cauchy (μ ...
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 which has one shape parameter (and a scale parameter).
The chi-squared distribution is a special case of the gamma distribution, in that (,) using the rate parameterization of the gamma distribution (or (,) using the scale parameterization of the gamma distribution) where k is an integer.
Guanine nucleotide-binding protein G(I)/G(S)/G(O) subunit gamma-2 is a protein that in humans is encoded by the GNG2 gene. [5] [6] Heterotrimeric G proteins play vital roles in cellular responses to external signals. The specificity of a G protein-receptor interaction is primarily mediated by the gamma subunit.[supplied by OMIM] [6]
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function 1 / Γ(z) is an entire function.
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Plot of the hypergeometric function 2F1(a,b; c; z) with a=2 and b=3 and c=4 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics , the Gaussian or ordinary hypergeometric function 2 F 1 ( a , b ; c ; z ) is a special function represented by the hypergeometric series , that ...