- #1
Mogarrr
- 120
- 6
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.
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.