Paper Info
Title
Some new statistical methods for a class of zero-truncated discrete distributions with applications
Abstract
AbstractCounting data without zero category often occurs in various fields. A class of zero-truncated discrete distributions such as the zero-truncated Poisson, zero-truncated binomial and zero-truncated negative-binomial distributions are proposed in literature to model such count data. In this paper, three main contributions have been made for better studying the zero-truncated discrete distributions: First, a novel unified expectation---maximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zero-truncated discrete distributions and an important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EM-type algorithms; Second, for those who do not understand the principle of latent variables, a unified minorization---maximization algorithm, as an alternative to the EM algorithm, for obtaining the MLEs of parameters in a class of zero-truncated discrete distributions is discussed; Third, a unified method is proposed to derive the distribution of the sum of i.i.d.zero-truncated discrete random variables, which has important applications in the construction of the shortest Clopper---Pearson confidence intervals of parameters of interest and in the calculation of the exact p value of a two-sided test for small sample sizes in one sample problem.
Year
DOI
Venue
2019
10.1007/s00180-018-00860-0
Periodicals
Keywords
DocType
Volume
EM algorithm,MM algorithm,Shortest confidence intervals,Stochastic representation,Zero-truncated discrete models
Journal
34
Issue
ISSN
Citations 
3
0943-4062
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Guo-Liang Tian100.34
Xiqian Ding200.34
Yin Liu321.78
Man-Lai Tang400.34