A most unprincipled derivation of the gamma distribution

July 13, 2021

Introduction # In this article I will derive the gamma distribution in a most unprincipled way. Why? First, there are many good resources out there explaining how to derive the gamma distribution from first principles, usually involving these idealized things called poisson processes. These are great sources and I would definitely recommend them. This one by Aerin Kim is amazing. However, more often than not, people use gamma distributions in real world problems for much more mundane reasons: It’s a well behaved yet flexible positive continuous distribution. ...