Generalized Linear Model/Examples/Poisson Distribution

Example of Generalized Linear Model

Let $Y$ be a random variable with a Poisson distribution.

Let $Y$ have an expectation $\lambda$ which varies with $x$.

Then the link function $\map g \lambda$ of the generalized linear model for $Y$ is given by:

$\map g \lambda = \ln \lambda$

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