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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:
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).
Gamma correction is a type of power law function whose exponent is the Greek letter gamma (γ). It should not be confused with the mathematical Gamma function. The lower case gamma, γ, is a parameter of the former; the upper case letter, Γ, is the name of (and symbol used for) the latter (as in Γ(x)). To use the word "function" in ...
File:Gamma_distribution_pdf.png licensed with Cc-by-sa-3.0-migrated, GFDL, GPL 2005-03-10T20:34:05Z MarkSweep 1300x975 (162472 Bytes) new version of PDF and matching CDF; 2005-03-10T17:45:44Z Cburnett 960x720 (138413 Bytes) Probability density function for the Gamma distribution {{GFDL}} Uploaded with derivativeFX
A proof is given below in § Relationship to the gamma function. The beta function is also closely related to binomial coefficients. When m (or n, by symmetry) is a positive integer, it follows from the definition of the gamma function Γ that [1] (,) = ()! ()!
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
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