Overview
The exponential family of distributions is a listing of statistical distributions that can be put into a pre-defined form, including the following:
- Bernoulli
- Multinoulli
- Gaussian
- Poisson
Different authors express the form of the exponential family differently. Below is the form given in Hardin.
{% f(y; \theta, \phi) = exp[\frac{y \theta - b(\theta)}{a(\phi)} + c(y,\phi)] %}
The advantage of stating a distribution in the exponential family form is that, any derivation that applies to the exponential
family will apply to all distributions that are in the exponential family. This includes the standard techniques for
fitting a distribution to a dataset.