GLM for Count Data

Generalized linear models for count data are regression techniques available for modeling outcomes describing a type of discrete data where the occurrence might be relatively rare. A common distribution for such a random variable is Poisson.

The probability that a variable Y with a Poisson distribution is equal to a count value
$${ P(Y = y) = {{\lambda^y e^{-\lambda}} \over {y!}}}  y = 0, 1, 2, ..., \infty $$
where \( \lambda \) is the average count called the rate