Certain estimation problems for multivariate hypergeometric models

Abstract

Certain estimation problems associated with the multivariate hypergeometric models: the property of completeness, maximum likelihood estimates of the parameters of multivariate negative hypergeometric, multivariate negative inverse hypergeometric, Bayesian estimation of the parameters of multivariate hypergeometric and multivariate inverse hypergeometrics are discussed in this paper.A two stage approach for generating the prior distribution, first by setting up a parametric super population and then choosing a prior distribution is followed. Posterior expectations and variances of certain functions of the parameters of the finite population are provided in cases of direct and inverse sampling procedures. It is shown that under extreme diffuseness of prior knowledge the posterior distribution of the finite population mean has an approximate mean ~ and variance (N-n)S2/Nn, providing a Bayesian interpretation for the classical unbiased estimates in traditional sample survey theory.

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“…If we take out balls at random without replacement, it follows that the number of balls of each color = 1, … , in the resulting sample has the multivariate hypergeometric distribution. Consequently, the probability for obtaining a specific composition of colored balls in the sample can be derived as follows [15][16]:…”