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Multivariate Polya and Inverse Polya Distributions of Order k
Author(s) -
Philippou A. N.,
Tripsiannis G. A.
Publication year - 1991
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710330214
Subject(s) - mathematics , multinomial distribution , dirichlet distribution , multivariate statistics , negative binomial distribution , inverse wishart distribution , inverse , poisson distribution , hypergeometric distribution , statistics , multivariate normal distribution , negative multinomial distribution , binomial (polynomial) , combinatorics , beta binomial distribution , mathematical analysis , geometry , boundary value problem
Multivariate Polya and inverse Polya distributions of order k are derived by means of generalized urn models and by compounding the type II multinomial and multivariate negative binomial distributions of order k of P HILIPPOU , A NTZOULAKOS and T RIPSIANNIS (1990, 1988), respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a multivariate hypergeometric distribution of order k , a negative one, an inverse one, a negative inverse one and a discrete uniform of the same order. The probability generating functions, means, variances and covariances of the new distributions are obtained and five asymptotic results are established relating them to the above‐mentioned multinomial and multivariate negative binomial distributions of order k , and to the type II negative binomial and the type I multivariate Poisson distributions of order k of P HILIPPOU (1983), and P HILIPPOU , A NTZOULAKOS and T RIPSIAN‐NIS (1988), respectively. Potential applications are also indicated. The present paper extends to the multivariate case the work of P HILIPPOU , T RIPSIANNIS and A NTZOULAKOS (1989) on Polya and inverse Polya distributions of order k. .