Notes on Poisson Regression and Some Extensions Dan Powers Soc385K Fall 07 Poisson Regression. The Poisson distribution is the most common probability distribution for count data. The Poisson probability model is appropriate for events that occur randomly over time and/or space. The probability function for Y is given by Pr(Y = y|µ) = e−µµy y! y ≥ 0, µ > 0 (1) Usually, we will be interested in es