A Generalized Bivariate Geometric Distribution Based on an Urn Model with Stochastic Replacement

Abstract

A Generalized Bivariate Geometric Distribution (GBGD) for explaining data arisen from four-fold sampling has been obtained through an urn-model with stochastic replacement. The marginal distributions of this generalized distribution, as in the case of the Bivariate Geometric Distribution (BGD), are the geometric distributions, but its one of the conditional distributions is the Consul’s (1974) Quasi Binomial Distribution (QBD), in place of binomial distribution in the BGD. The moments of the first and second orders of the GBGD have been obtained. As the QBD has been found to possess tremendous capability to fit to discrete data-sets of various nature, it is expected that the obtained GBGD would cover a wide range of data-sets.

Keywords and phrases. Urn –Model, Marginal and Conditional Distributions, Generalized Bivariate Geometric Distribution, Drawing with Replacement, Quasi Binomial Distribution, Additional Parameters.

2000 Mathematics Subject Classification. 62E05, 62E99