GAMMA distribution

A continuous random variable is said to have a gamma distribution if its probability density can be written in the form f(t) = a(at)^b−1 e ^−at/Γ(b) where a and b are any positive real numbers and Γ(b) is the gamma function evaluated at b. The constant b is called the shape parameter, while a (or various equivalents) is called the scale parameter. If b happens to be a positive integer, then Γ (b) = (b − 1)! and this gamma distribution is also called an Erlang distribution. Furthermore, if b is either an integer or half-integer (1/2, 3/2, etc.) and a = 1/2, the resultant gamma distribution is equivalent to the classical χ² distribution of statistics. Erlang distribution.