Exponential Family of Distributions
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 stsating 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.
Formulations
