Multivariate Polya and Inverse Polya Distributions of Orderk
Andreas N. Philippou, Gregory A. Tripsiannis · Biometrical Journal · 1991
Abstract Multivariate Polya and inverse Polya distributions of orderkare derived by means of generalized urn models and by compounding the type II multinomial and multivariate negative binomial distributions of orderkof PHILIPPOU, ANTZOULAKOSand TRIPSIANNIS(1990, 1988), respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a multivariate hypergeometric distribution of orderk, 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 orderk, and to the type II negative binomial and the type I multivariate Poisson distributions of orderkof PHILIPPOU(1983), and PHILIPPOU, ANTZOULAKOSand TRIPSIAN‐NIS(1988), respectively. Potential applications are also indicated. The present paper extends to the multivariate case the work of PHILIPPOU, TRIPSIANNISand ANTZOULAKOS(1989) on Polya and inverse Polya distributions of orderk..