An Introduction to Discrete-Valued Time Series

Appendix A

Examples of Count Distributions

This appendix provides a brief survey of common models for count data and their stochastic properties. In particular, we discuss dispersion properties and types of generating functions, the latter being useful tools when analyzing count models. The presented models are divided into univariate and multivariate models, and into models for an infinite range like or a finite range like .

A.1 Count Models for an Infinite Range

The most famous model for a count random variable having the range (full set of non-negative integers) is the Poisson distribution.

Example A.1.1 (Poisson distribution)

The Poisson distribution with parameter is defined by the pmf

From its generating functions (also see Table 2.2 ),

the characteristic equi-cumulant property ...