ABSTRACT
Consider again the observed earthquake series displayed in Figure 1.1 on p. 4. The observations are unbounded counts, making the Poisson distribution a natural choice to describe them. However, the sample variance of the observations is substantially greater than the sample mean, indicating overdispersion relative to the Poisson. In Exercise 1 of Chapter 1 we saw that one can accommodate overdispersion by using a mixture model, specifically a mixture of Poisson distributions for this series.
