Exponential Family

Gist

Definition

Any distribution whose density can be written as:

where:

• $\theta$ is the canonical parameter
• $b(\theta )$ is the twice differentiable function
• $\varphi$ is a dispersion parameter
• $w$ is a known weight
• $c$ is a normalizing constant

Members

1. Normal
2. Exponential
3. Binomial
4. Poisson

Uses

Explains why we can use these probability distributions for the Generalized linear models (GLM)