Classes of Multivariate Exponential and Multivariate Geometric Distributions Derived from Markov Processes

Author(s):

Longford, Nicholas T.

Publication Year:

1989

Report Number:

RR-89-13

Source:

ETS Research Report

Document Type:

Report

Page Count:

19

Subject/Key Words:

Markov Processes, Multivariate Analysis, Statistical Distributions

Abstract

A class of multivariate exponential distributions as the distributions of occupancy times in upwards skip-free Markov processes in continuous time is defined. These distributions are infinitely divisible, and the multivariate Gamma class defined by convolutions and fractions is a substantial generalization of the class defined by Johnson & Kotz (1972). Parallel classes of multivariate geometric and multivariate negative binomial distributions are constructed from occupancy times in 'instant' upwards skip-free Markov chains. Maximum likelihood estimation and times series applications are discussed. (19pp.)

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• http://dx.doi.org/10.1002/j.2330-8516.1989.tb00339.x