Loss Models, 5th Edition

Appendix AAn Inventory of Continuous Distributions

A.1 Introduction

Descriptions of the models are given starting in Section A.2. First, a few mathematical preliminaries are presented that indicate how the various quantities can be computed.

The incomplete gamma function¹ is given by

with

A useful fact is . Also, define

At times, we will need this integral for nonpositive values of . Integration by parts produces the relationship

This process can be repeated until the first argument of G is , a positive number. Then, it can be evaluated from

However, if is a negative integer ...