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

Longford, Nicholas T.
Publication Year:
Report Number:
RR-89-13, PSRTR-89-87
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Markov Processes, Multivariate Analysis, Statistical Distributions


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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