Distribution of Random Variable in Generalized Linear Model is Exponential

Theorem

Let $Y$ be a random variable of a generalized linear model.

Then $Y$ is a member of the exponential family of probability distributions.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generalized linear models
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generalized linear models