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postgraduate thesis: Some new statistical methods for a class of zerotruncated discrete distributions with applications
Title  Some new statistical methods for a class of zerotruncated discrete distributions with applications 

Authors  
Issue Date  2015 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Ding, X. [丁茜茜]. (2015). Some new statistical methods for a class of zerotruncated discrete distributions with applications. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5481903 
Abstract  Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenuretracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zerotruncated discrete models such as zerotruncated Poisson, zerotruncated binomial and zerotruncated negativebinomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zerotruncated discrete distributions.
In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zerotruncated distribution random variables, which has important applications in the construction of the shortest ClopperPerson confidence intervals of parameters of interest and in the calculation of the exact pvalue of a twosided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectationmaximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zerotruncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EMtype algorithms. In addition, a unified minorizationmaximization (MM) algorithm for obtaining the MLEs of parameters in a class of zerotruncated discrete distributions is provided.
The first objective of Chapter 3 is to propose the multivariate zerotruncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any rdimensional subvector of the multivariate ZTCS random vector of dimension m is an rdimensional zerodeated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zeroadjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data. 
Degree  Master of Philosophy 
Subject  Distribution (Probability theory) 
Dept/Program  Statistics and Actuarial Science 
Persistent Identifier  http://hdl.handle.net/10722/211126 
DC Field  Value  Language 

dc.contributor.author  Ding, Xiqian   
dc.contributor.author  丁茜茜   
dc.date.accessioned  20150707T23:10:43Z   
dc.date.available  20150707T23:10:43Z   
dc.date.issued  2015   
dc.identifier.citation  Ding, X. [丁茜茜]. (2015). Some new statistical methods for a class of zerotruncated discrete distributions with applications. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5481903   
dc.identifier.uri  http://hdl.handle.net/10722/211126   
dc.description.abstract  Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenuretracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zerotruncated discrete models such as zerotruncated Poisson, zerotruncated binomial and zerotruncated negativebinomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zerotruncated discrete distributions. In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zerotruncated distribution random variables, which has important applications in the construction of the shortest ClopperPerson confidence intervals of parameters of interest and in the calculation of the exact pvalue of a twosided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectationmaximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zerotruncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EMtype algorithms. In addition, a unified minorizationmaximization (MM) algorithm for obtaining the MLEs of parameters in a class of zerotruncated discrete distributions is provided. The first objective of Chapter 3 is to propose the multivariate zerotruncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any rdimensional subvector of the multivariate ZTCS random vector of dimension m is an rdimensional zerodeated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zeroadjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  Creative Commons: Attribution 3.0 Hong Kong License   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.subject.lcsh  Distribution (Probability theory)   
dc.title  Some new statistical methods for a class of zerotruncated discrete distributions with applications   
dc.type  PG_Thesis   
dc.identifier.hkul  b5481903   
dc.description.thesisname  Master of Philosophy   
dc.description.thesislevel  Master   
dc.description.thesisdiscipline  Statistics and Actuarial Science   
dc.description.nature  published_or_final_version   