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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 Gamma distribution, which describes the time until n consecutive rare random events occur in a process with no memory. The Erlang distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems; The inverse-gamma distribution; The generalized gamma distribution
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).
Inverse gamma distribution is a special case of type 5 Pearson distribution; A multivariate generalization of the inverse-gamma distribution is the inverse-Wishart distribution. For the distribution of a sum of independent inverted Gamma variables see Witkovsky (2001)
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
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to (;,,) (()) (| |),where D is a parabolic cylinder function. [1]As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,
In statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart , who first formulated the distribution in 1928. [ 1 ]
The gamma distribution is a natural conjugate prior to a Gompertz likelihood with known, ... "Implementing the Gamma/Gompertz/NBD Model in MATLAB" (PDF). Cergy ...