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

equation

with

equation

A useful fact is img. Also, define

equation

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

equation

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

equation

However, if img is a negative integer ...

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