A Family of Finite Mixture Distributions for Modelling Dispersion in Count Data

Seng Huat Ong (), Shin Zhu Sim, Shuangzhe Liu and Hari M. Srivastava ()
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Seng Huat Ong: Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia
Shin Zhu Sim: School of Mathematical Sciences, University of Nottingham Malaysia, Semenyih 43500, Malaysia
Shuangzhe Liu: Faculty of Science and Technology, University of Canberra, Bruce, ACT 2617, Australia
Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada

Stats, 2023, vol. 6, issue 3, 1-14

Abstract: This paper considers the construction of a family of discrete distributions with the flexibility to cater for under-, equi- and over-dispersion in count data using a finite mixture model based on standard distributions. We are motivated to introduce this family because its simple finite mixture structure adds flexibility and facilitates application and use in analysis. The family of distributions is exemplified using a mixture of negative binomial and shifted negative binomial distributions. Some basic and probabilistic properties are derived. We perform hypothesis testing for equi-dispersion and simulation studies of their power and consider parameter estimation via maximum likelihood and probability-generating-function-based methods. The utility of the distributions is illustrated via their application to real biological data sets exhibiting under-, equi- and over-dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM–Poisson distributions for handling under-, equi- and over-dispersion in count data.

Keywords: convolution; dispersion; Conway–Maxwell–Poisson; generalized Poisson; inverse trinomial; negative binomial; goodness-of-fit; log-concavity; parameter estimation; score and likelihood ratio tests (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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