Bayesian Statistics: An Introduction, 4th Edition

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 ...