Exponential Family

Gist

Explains why we have the Generalized linear models (GLM) at all.

Definition

Any probability 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 Distribution
2. Exponential Distribution
3. Binomial Distribution
4. Poisson Distributions

Uses

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