Consider our loss-ALAE dataset, and - as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, > library(evd) > data(lossalae) > Z=lossalae > X=Z;Y=Z ...

A common model for counts data is the Poisson. There are cases however that we only record positive counts, ie there is a truncation of 0. This is the truncated Poisson model. To study this model we only need the total counts and the sample size. This comes from the sufficient statistic principle as the