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, but their distribution is clearly overdispersed relative to the Poisson. We saw in Chapter 1 that this feature can be accommodated by using a mixture of Poisson distributions with means λ1, λ2, …, λ m . The choice of mean is made by a second random process, the parameter process. The mean λ i is selected with probability δ i , where i = 1, 2,…, m and ∑ i = 1 m δ i = 1 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315372488/1d497297-7329-489f-a690-fa5bd69bcfba/content/eq105.tif"/> .