Definition:Exponential Family of Distributions

Definition

Let $P$ be a probability distribution.

$P$ is a member of the exponential family of distributions if and only if it has a probability density function of the form:

$\map f {x, h} = \map \exp {\map a x \map b h + \map c h + \map d x}$

where $h$ is a parameter whose value is to be determined.

Also see

• Definition:Generalized Linear Model

• Definition:Normal Distribution
• Definition:Poisson Distribution
• Definition:Binomial Distribution

• Results about the exponential family of distributions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): exponential family of distributions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): exponential family of distributions