南方科技大学知识苑(SUSTech KC): Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms

题名	Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms
作者	Li, Xun-Jian1 ; Tian, Guo-Liang1 ; Zhang, Mingqian 1; Ho, George To Sum 2; Li, Shuang3
通讯作者	Li, Shuang
发表日期	2023-03-01
DOI	10.3390/math11061478
发表期刊	MATHEMATICS 影响因子和分区
EISSN	2227-7390
卷号	11 期号:6
摘要	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.
关键词	generalized Poisson distribution mean regression model MM algorithms over-dispersion under-dispersion
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一 ; 通讯
资助项目	National Natural Science Foundation of China[12171225] ; Research Grants Council of Hong Kong[UGC/FDS14/P05/20]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000957724300001
出版者	MDPI
来源库	Web of Science
引用统计	被引频次[WOS]：3
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/523992
专题	理学院_统计与数据科学系理学院_数学系
作者单位	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
第一作者单位	统计与数据科学系
通讯作者单位	数学系
第一作者的第一单位	统计与数据科学系
推荐引用方式 GB/T 7714	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).
APA	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).
MLA	Li, Xun-Jian,et al."Modeling Under-Dispersed Count Data by the Generalized Poisson Distribution via Two New MM Algorithms".MATHEMATICS 11.6(2023).