Type I multivariate zero-truncated/adjusted Poisson distributions with applications

Tian, Guo-Liang1; Liu, Yin2; Tang, Man-Lai3; Jiang, Xuejun1

2018-12-15

10.1016/j.cam.2018.05.014

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS   影响因子和分区

0377-0427

1879-1778

Although there is substantial literature on the univariate zero-truncated Poisson (ZTP) distributions, few works have been done for developing multivariate ZTP distributions with dimension larger than two. In this paper, we first propose a new Type I multivariate ZTP distribution to model multivariate zero-truncated count data and develop its important distributional properties, while providing efficient statistical inference methods. The key idea for extending the univariate ZTP distribution to a multivariate version is to identify a new stochastic representation of the ZTP random variable, resulting in a novel expectation-maximization algorithm with a feature that the introduced latent variables are independent of the observed variables. Since the ZTP distribution is closely related with the zero-adjusted Poisson (ZAP) distribution, the second objective of this paper is to propose a new family of Type I multivariate ZAP distributions (including the Type I multivariate ZTP distribution, the Type I multivariate zero-inflated Poisson (ZIP) distribution, the Type I multivariate zero-deflated Poisson (ZDP) distribution as its special cases) by accounting for truncation, inflation and deflation at zero. The corresponding distributional properties are explored and the associated statistical methods are provided. Finally, three real data sets are used to illustrate the proposed distributions and corresponding analysis methods. (C) 2018 Elsevier B.V. All rights reserved.

Expectation-maximization algorithm Multivariate zero-adjusted Poisson model Multivariate zero-truncated Poisson model Stochastic representation

SCI ; EI

英语

第一

Shenzhen Sci-Tech Fund[JCYJ20170307110329106]

Mathematics

Mathematics, Applied

WOS:000440394900010

ELSEVIER SCIENCE BV

20182305280904

Statistical methods ; Stochastic models ; Stochastic systems ; Transport properties

Probability Theory:922.1 ; Mathematical Statistics:922.2 ; Physical Properties of Gases, Liquids and Solids:931.2 ; Systems Science:961

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
2.Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China
3.Hang Seng Management Coll, Sch Business, Dept Math & Stat, Shatin, Hong Kong, Peoples R China

Tian, Guo-Liang,Liu, Yin,Tang, Man-Lai,et al. Type I multivariate zero-truncated/adjusted Poisson distributions with applications[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2018,344:132-153.

Tian, Guo-Liang,Liu, Yin,Tang, Man-Lai,&Jiang, Xuejun.(2018).Type I multivariate zero-truncated/adjusted Poisson distributions with applications.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,344,132-153.

Tian, Guo-Liang,et al."Type I multivariate zero-truncated/adjusted Poisson distributions with applications".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 344(2018):132-153.