# The Gamma distribution

2021 Jun 10 See all posts

## TODO

• What is the gamma distribution

• Derive PDF as a limit of negative binomial
• Generalize factorial using the gamma function
• Show it is the sum of i.i.d Expo$(\lambda)$ via convolution (not MGF if possible)
• Show how the gamma is the conjugate prior of Pois$(\lambda)$

• Give an intuitive connection between $\lambda$ ~ Gamma$(y, t)$ and $T_n$ ~ Gamma$(n, \lambda)$ explaining why they represent the same thing

• Gamma AND Beta? change post to introduce both?