# Exponential Family of Distributions

1. Aug 13, 2014

### Mogarrr

I'm reading about the exponential family of distributions. In my book, I have the expression

$f(x|\theta) = h(x)c(\theta)exp(\sum_{i=1}^{k} w_i(\theta) t_i(x))$

where $h(x) \geq 0$, $t_1(x), t_2(x),...,t_k(x)$ are real valued functions of the observation $x$, $c(\theta) \geq 0$, and $w_1(\theta),w_2(\theta),...,w_k(\theta)$ are real-valued functions of the possibly vector-valued parameter $\theta$.

What's being stressed in the few examples available (in the book), is the indicator function. Here's the indicator function:

$I_A(x) = 1$, if $x \in A$, and $I_A(x) = 0$, if $x \notin A$, where $A$ is the set values the observation or parameter may take.

What I'm seeing, is that the indicator function is inserted with $h(x)$ or $c(\theta)$ whenever these functions are constants.

Do you guys know of any examples where an indicator function is used and $h(x)$ or $c(\theta)$ are not constants?

I'm thinking the whole point of using indicator functions is to make the expression exactly like the probability distribution function.

2. Aug 21, 2014