Discrete multivariate distributions (original) (raw)

A family of multivariate discrete distributions

South African Statistical Journal, 2020

In this short paper, the multivariate Poisson-Gamma, the multinomial N-mixture and the negative multinomial distributions are shown to have probability mass functions of the same form and thus to share, broadly, the same distributional properties. The three distributions are, however, fundamentally very different in nature, that is, in terms of genesis, interpretation and model building, and these differences are highlighted and discussed.

A unified approach to bivariate discrete distributions

Metrika, 2007

Here we introduce a bivariate generalized hypergeometric factorial moment distribution (BGHFMD) through its probability generating function (p.g.f.) whose marginal distributions are the generalized hypergeometric factorial moment distributions introduced by Kemp and Kemp (Bull Int Stat Inst 43:336-338,1969). Well-known bivariate versions of distributions such as binomial, negative binomial and Poisson are special cases of this distribution. A genesis of the distribution and explicit closed form expressions for the probability mass function of the BGHFMD, its factorial moments and the p.g.f.'s of its conditional distributions are derived here. Certain recurrence relations for probabilities, moments and factorial moments of the bivariate distribution are also established.

A Generalization to the Family of Discrete Distributions

An alternative approaches for a couple of discrete distributions like Binomial and Multinomial, Poisson, etc having more general form of sampling method (more than one outcome in one trial) compared to tradition sampling heuristics have been suggested and termed as Generalized Binomial, Generalized Multinomial, Generalized Poisson, Generalized Geometric respectively. It is evident that the traditional existing distributions are the special cases of the proposed generalized distributions. The basic distributional properties of the proposed distributions have also been examined including the limiting form. Real life examples are cited for the respective distributions.

Some representations of the multivariate Bernoulli and binomial distributions

Journal of Multivariate Analysis, 1990

Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the concept of Kronecker product from matrix calculus. The multivariate Bernoulli distribution entails a parameterized model, that provides an alternative to the traditional log-linear model for binary variables.