In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. It has a scale parameter a and a shape parameter b. If b is an integer then the distribution represents the sum of b exponentially distributed random variables, each of which has parameter a.

The probability density function of the gamma distribution is

f(x,a,b) = exp ( (a-1) * log (x/b) - x/b-log (gamma (a) ) ) / b

where   

gamma(x) = integral from 0 to inf of t^(x-1)* exp(-t) dt.

support -Inf ⇐ x ⇐ Inf