Loss Models, 5th Edition

Appendix BAn Inventory of Discrete Distributions

B.1 Introduction

The 16 models presented in this appendix fall into three classes. The divisions are based on the algorithm used to compute the probabilities. For some of the more familiar distributions, these formulas will look different from the ones you may have learned, but they produce the same probabilities. After each name, the parameters are given. All parameters are positive unless otherwise indicated. In all cases, is the probability of observing k losses.

For finding moments, the most convenient form is to give the factorial moments. The jth factorial moment is . We have and .

The estimators presented are not intended to be useful estimators but, rather, provide starting values for maximizing the likelihood (or other) function. For determining starting values, the following quantities are used (where is the observed frequency at k [if, for the last entry, represents the number of observations at k or more, assume it was ...