Advances and Applications in Statistics
Volume 7, Issue 1, Pages 141 - 156
(April 2007)
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MULTIVARIATE GENERALIZED RUN-RELATED DISTRIBUTIONS
G. A. Tripsiannis (Greece), A. N. Philippou (Greece) and A. A. Papathanasiou (Greece)
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Abstract: A multivariate generalized negative binomial distribution of order k, which extends to the multivariate case the generalized negative binomial distribution of order k of Tripsiannis et al. [21] and to distributions of order k the multivariate generalized negative binomial distribution of Jain [3], is presently derived and studied by means of combinatorial methods. This run-related distribution gives rise to new multivariate generalized logarithmic, Borel-Tanner and Polya distributions of the same order. The latter includes as special cases several new multivariate distributions of order k and generalizes the multivariate generalized Polya distribution of Sen and Jain [16]. An application of the multivariate generalized negative binomial distribution of order k is given in the theory of queues, and a few graphs of it are presented for |
Keywords and phrases: multivariate distributions of order k, generalized, lattice paths, negative binomial, logarithmic series, Borel-Tanner, Polya, mean, variance-covariance, theory of queues, graphs. |
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