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Generalized endpoint-inflated binomial model
Tian, Guo-Liang1; Ma, Huijuan2,4; Zhou, Yong3,4; Deng, Dianliang5
AbstractTo model binomial data with large frequencies of both zeros and right-endpoints, Deng and Zhang (in press) recently extended the zero-inflated binomial distribution to an endpoint-inflated binomial (EIB) distribution. Although they proposed the EIB mixed regression model, the major goal of Deng and Zhang (2015) is just to develop score tests for testing whether endpoint-inflation exists. However, the distributional properties of the EIB have not been explored, and other statistical inference methods for parameters of interest were not developed. In this paper, we first construct six different but equivalent stochastic representations for the EIB random variable and then extensively study the important distributional properties. Maximum likelihood estimates of parameters are obtained by both the Fisher scoring and expectation-maximization algorithms in the model without covariates. Bootstrap confidence intervals of parameters are also provided. Generalized and Fixed EIB regression models are proposed and the corresponding computational procedures are introduced. A real data set is analyzed and simulations are conducted to evaluate the performance of the proposed methods. All technical details are put in a supplemental document (see Appendix A). (C) 2015 Elsevier B.V. All rights reserved.
KeywordEndpoint-inflated binomial distribution Expectation-maximization algorithm Multinomial logistic regression model Stochastic representation Zero-inflated binomial distribution
Funding ProjectNational Natural Science Foundation of China (NSFC)[71271128] ; State Key Program of National Natural Science Foundation of China[71331006] ; NCMIS, Key Laboratory of RCSDS, CAS ; Shanghai University of Finance and Economics through Project 211 Phase IV, Shanghai First-class Discipline A ; Natural Sciences and Engineering Research Council of Canada ; IRTSHUFE, PCSIRT[IRT13077]
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Interdisciplinary Applications ; Statistics & Probability
WOS IDWOS:000357348000008
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Document Type期刊论文
Corresponding AuthorMa, Huijuan
Affiliation1.Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China
2.Univ Sci & Technol China, CM0FL, Hefei 230026, Anhui, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
4.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai, Peoples R China
5.Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada
Recommended Citation
GB/T 7714
Tian, Guo-Liang,Ma, Huijuan,Zhou, Yong,et al. Generalized endpoint-inflated binomial model[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS,2015,89:97-114.
APA Tian, Guo-Liang,Ma, Huijuan,Zhou, Yong,&Deng, Dianliang.(2015).Generalized endpoint-inflated binomial model.COMPUTATIONAL STATISTICS & DATA ANALYSIS,89,97-114.
MLA Tian, Guo-Liang,et al."Generalized endpoint-inflated binomial model".COMPUTATIONAL STATISTICS & DATA ANALYSIS 89(2015):97-114.
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