5.3 Exponential family

Most or all of the distributions we will use for this class come from the exponential family of distributions.

The exponential family is very flexible, and whether you know it or not, it includes most of the distributions one might use to describe every day phenomena. It includes most of the probability distributions with which you are familiar, and many more. Just ask this very reliable Wikipedia entry. Oh, let’s face it, you were going there anyway, I just cut out the Google step.

Take a look at the table at the bottom of this Wikipedia page just to get an idea of how many distributions are included within the exponential! Holy cow! We’re not going to look at all of these in this class- I just want you to be aware that this is a huge family of specific distributions.

Distributions that we’ll focus on in this chapter:

1. Continuous distributions
Normal (Gaussian)
Lognormal
Beta
Uniform

2. Discrete distributions
Bernouli
Binomial
Multinomial
Poisson
Negative binomial