Chapter Preview. In this chapter, the dependent variable y is a count, taking on values 0, 1, 2 and so on, that describes a number of events. Count dependent variables form the basis of actuarial models of claims frequency. In other applications, a count dependent variable may be the number of accidents, the number of people retiring or the number of firms becoming insolvent.
The chapter introduces Poisson regression, a model that includes explanatory variables with a Poisson distribution for counts. This fundamental model handles many datasets of interest to actuaries. However, with the Poisson distribution, the mean equals the variance, a limitation suggesting the need for more general distributions such as the negative binomial. Even the two parameter negative binomial can fail to capture some important features, motivating the need for even more complex models such as the “zero-inflated” and latent variable models introduced in this chapter.