Title  Mean regression model for the zerotruncated Poisson distribution and its generalization 
Author  
Corresponding Author  Shi，Jianhua 
Publication Years  20230301

DOI  
Source Title  
ISSN  01679473

Volume  179 
Abstract  Zerotruncated count data (e.g., days of staying in hospital; survival weeks of female patients with breast cancer) often arise in various fields such as medical studies. To model such data, the zerotruncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients β or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of β. This paper aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of a challenge that the original Poisson mean parameter λ cannot be expressed explicitly by the ZTP mean parameter μ, an embedded Newton–Raphson algorithm is developed to calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests (i.e., the likelihood ratio test, the Wald test and the score test) are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the ktruncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods. 
Keywords  
URL  [Source Record] 
Language  English

SUSTech Authorship  First

Funding Project  National Natural Science Foundation of China[12171225];Natural Science Foundation of Fujian Province[2020J01794];

ESI Research Field  MATHEMATICS

Scopus EID  2s2.085140748505

Data Source  Scopus

Citation statistics 
Cited Times [WOS]:0

Document Type  Journal Article 
Identifier  http://kc.sustech.edu.cn/handle/2SGJ60CL/407075 
Department  Department of Statistics and Data Science 
Affiliation  1.Department of Statistics and Data Science,Southern University of Science and Technology,Shenzhen,Guangdong Province,518055,China 2.Department of Statistics and Data Science,Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science,BNU–HKBU United International College,Zhuhai,Guangdong Province,519087,China 3.School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian Province,363000,China 
First Author Affilication  Department of Statistics and Data Science 
First Author's First Affilication  Department of Statistics and Data Science 
Recommended Citation GB/T 7714 
Li，Xun Jian,Sun，Yuan,Tian，Guo Liang,et al. Mean regression model for the zerotruncated Poisson distribution and its generalization[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2023,179.

APA 
Li，Xun Jian,Sun，Yuan,Tian，Guo Liang,Liang，Jiajuan,&Shi，Jianhua.(2023).Mean regression model for the zerotruncated Poisson distribution and its generalization.COMPUTATIONAL STATISTICS & DATA ANALYSIS,179.

MLA 
Li，Xun Jian,et al."Mean regression model for the zerotruncated Poisson distribution and its generalization".COMPUTATIONAL STATISTICS & DATA ANALYSIS 179(2023).

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