Search

The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in reliability, fraction defective in quality control, and the number of initial faults present in software coding. Recently, Borges et al. considered a COM type generalization of the binomial distribution, called COM–Poisson–Binomial (CMPB) and investigated many of its characteristics and some interesting applications. In the same spirit, we develop here a generalization of the hypergeometric distribution, called the COM–hypergeometric distribution. We discuss many of its characteristics such as the limiting forms, the over- and underdispersion, and the behavior of its failure rate. We write its probability-generating function (pgf) in the form of Kemp's family of distributions when the newly introduced shape parameter is a positive integer. In this form, closed-form expressions are derived for its mean and variance. Finally, we develop statistical inference procedures for the model parameters and illustrate the results by extensive Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

A modification of the quadratic form involved in a generalized minimum chi-squared procedure yields the same asymptotic null distribution of the test statistic for testing fit by an assumed model, but a different form of nonnull distribution emerges. This result is applied to testing fit of the negative binomial and Neyman Type A distributions, and tables of asymptotic power are presented that show the increase of power obtained. A numerical example is presented to illustrate the technique. [ABSTRACT FROM AUTHOR]