From AMS Glossary
A continuous random variable x is said to have a gamma distribution if the range of x consists of all positive real numbers and if x possesses a density function f(x) that satisfies the equation
where β and p are positive numbers and where Γ is the gamma function defined by the integral
for p > 0.
The mean of the density function is βp, and the standard deviation is β(p)½. The gamma distribution, which is a special case of the Pearson distribution, is skewed to the right. In meteorology, scalar multiples of the gamma distribution are used to represent size distributions of cloud drops.