Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms

Li, Xun-Jian1; Tian, Guo-Liang1; Zhang, Mingqian1; Ho, George To Sum2; Li, Shuang3

2023-03-01

10.3390/math11061478

MATHEMATICS   Impact Factor & Quartile

2227-7390

Under-dispersed count data often appear in clinical trials, medical studies, demography, actuarial science, ecology, biology, industry and engineering. Although the generalized Poisson (GP) distribution possesses the twin properties of under- and over-dispersion, in the past 50 years, many authors only treat the GP distribution as an alternative to the negative binomial distribution for modeling over-dispersed count data. To our best knowledge, the issues of calculating maximum likelihood estimates (MLEs) of parameters in GP model without covariates and with covariates for the case of under-dispersion were not solved up to now. In this paper, we first develop a new minimization-maximization (MM) algorithm to calculate the MLEs of parameters in the GP distribution with under-dispersion, and then we develop another new MM algorithm to compute the MLEs of the vector of regression coefficients for the GP mean regression model for the case of under-dispersion. Three hypothesis tests (i.e., the likelihood ratio, Wald and score tests) are provided. Some simulations are conducted. The Bangladesh demographic and health surveys dataset is analyzed to illustrate the proposed methods and comparisons with the existing Conway-Maxwell-Poisson regression model are also presented.

generalized Poisson distribution mean regression model MM algorithms over-dispersion under-dispersion

SCI

English

First ; Corresponding

National Natural Science Foundation of China[12171225] ; Research Grants Council of Hong Kong[UGC/FDS14/P05/20]

Mathematics

Mathematics

WOS:000957724300001

MDPI

Web of Science

1.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518055, Peoples R China
2.Hang Seng Univ Hong Kong, Dept Supply Chain & Informat Management, Shatin, Hong Kong, Peoples R China
3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

Li, Xun-Jian,Tian, Guo-Liang,Zhang, Mingqian,et al. Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms[J]. MATHEMATICS,2023,11(6).

Li, Xun-Jian,Tian, Guo-Liang,Zhang, Mingqian,Ho, George To Sum,&Li, Shuang.(2023).Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms.MATHEMATICS,11(6).

Li, Xun-Jian,et al."Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms".MATHEMATICS 11.6(2023).