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