A Conway Maxwell Poisson type generalization of the negative hypergeometric distribution. Issue 10 (18th May 2020)

• Record Type: Journal Article
• Authors: Roy, Sudip; Tripathi, Ram C.; Balakrishnan, Narayanaswamy
• Is Part Of: Communications in statistics. Volume 49:Issue 10(2020)
• Page Start: 2410
• Page End: 2428
• Publication Date: 2020-05-18
• Subjects: COM Poisson -- COMP-binomial -- negative hypergeometric distribution -- dispersion index -- failure rate -- shape parameter; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1576885
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: Negative hypergeometric distribution arises as a waiting time distribution when we sample without replacement from a finite population. It has applications in many areas such as inspection sampling and estimation of wildlife populations. However, as is well known, the negative hypergeometric distribution is over-dispersed in the sense that its variance is greater than the mean. To make it more flexible and versatile, we propose a modified version of negative hypergeometric distribution called COM-Negative Hypergeometric distribution (COM-NH) by introducing a shape parameter as in the COM-Poisson and COMP-Binomial distributions. It is shown that under some limiting conditions, COM-NH approaches to a distribution that we call the COM-Negative binomial (COMP-NB), which in turn, approaches to the COM Poisson distribution. For the proposed model, we investigate the dispersion characteristics and shape of the probability mass function for different combinations of parameters. We also develop statistical inference for this model including parameter estimation and hypothesis tests. In particular, we investigate some properties such as bias, MSE, and coverage probabilities of the maximum likelihood estimators for its parameters by Monte Carlo simulation and likelihood ratio test to assess shape parameter of the underlying model. We present illustrative data to provide discussion.