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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
In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities. It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level .
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).
In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices. [1] It is effectively a different parametrization of the Wishart distribution, and is used similarly, e.g. as the conjugate prior of the precision matrix of a multivariate normal distribution and matrix normal distribution.
The GIG distribution is also the basis for a number of wrapped distributions in the wrapped gamma family. [12] As being a special case of the generalized chi-squared distribution, there are many other applications; for example, in renewal theory [1] and in multi-antenna wireless communications. [13] [14] [15] [16]
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