Gamma distribution

The gamma distribution is a probability distribution that takes two parameters. The Erlang distribution and chi-squared distribution are both special cases of the gamma distribution.

Like the Erlang distribution, the gamma distribution's parameters are a shape parameter ${\displaystyle \alpha }$ and a rate parameter ${\displaystyle \beta }$. Unlike the Erlang distribution, ${\displaystyle \alpha }$ does not need to be an integer, because the gamma distribution is defined using the gamma function instead of the factorial.

The probability density function of the gamma distribution is $${\displaystyle f(x)={\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}x^{\alpha -1}e^{-\beta x}}$$