A Conway–Maxwell–Poisson Type Generalization of Hypergeometric Distribution

Sudip Roy (), Ram C. Tripathi () and Narayanaswamy Balakrishnan
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Sudip Roy: Department of Management Science and Statistics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA
Ram C. Tripathi: Department of Management Science and Statistics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA
Narayanaswamy Balakrishnan: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L8, Canada

Mathematics, 2023, vol. 11, issue 3, 1-15

Abstract: 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.

Keywords: hypergeometric; COM–Hypergeometric; COM–Poisson; COM–Poisson–Binomial; Kemp family of distributions; failure rate; reliability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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