Parameter Estimation for Certain q-Hypergeometric Distributions

Abstract

Various q-hypergeometric distributions have recently been described and examined in some detail in both the statistics and the quantum physics literatures. The q-hypergeometric distributions are of interest as q-analogues of a wide class of discrete distributions (the generalized hypergeometric probability distributions) which includes, for example, the Poisson, binomial, negative binomial and logarithmic distributions. The additional parameter q can be viewed as modifying the related standard distribution (the term deforming is used in the physics literature). Parameter estimation for the q-distributions has not received much attention. This paper examines the estimation problem with special reference to q-distributions related to the logarithmic distribution. Some simulation results for maximum-likelihood estimation are given.