Exponential Family
Overview
The exponential family of distributions is a class of statistical distributions that all share a common
form.
Properties
(
see Murphy)
Exponential Distribution Form
An exponential family distribution can be written in the following form.
{% f(y,\theta) = s(y) \times t(\theta) \times exp[a(y)b(\theta)] %}
This form can also be re-written as
{% f(y,\theta) = exp[a(y)b(\theta) + c(\theta) + d(y)] %}
where
{% s(y) = exp[d(y)] %}
{% t(\theta) = exp[c(\theta)] %}
