A.4 Gamma distribution
X has a (one-parameter) gamma distribution with parameter α, denoted
if it has density
This is simply another name for the distribution, we refer to as
If , then Y has a two-parameter gamma distribution with parameters α and β denoted
and it has density
so that its mean and variance are
This is simply another name for the distribution, we refer to as
If we recover the one-parameter gamma distribution; if so that the density is
we obtain another special case sometimes called the (negative) exponential distribution and denoted
The distribution function of any variable with a gamma distribution is easily found in terms of the incomplete gamma function
or in terms of Karl Pearson’s incomplete gamma function
Extensive tables can be found in Pearson (1924).