Some new statistical methods for a class of zero-truncated discrete distributions with applications

Tian, Guo-Liang1; Ding, Xiqian2; Liu, Yin3; Tang, Man-Lai4

2019-09

10.1007/s00180-018-00860-0

COMPUTATIONAL STATISTICS   影响因子和分区

0943-4062

1613-9658

Counting 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.

EM algorithm MM algorithm Shortest confidence intervals Stochastic representation Zero-truncated discrete models

SCI

英语

第一

[UGC/FDS14/P06/17]

Mathematics

Statistics & Probability

WOS:000476483900019

SPRINGER HEIDELBERG

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
2.Univ Hong Kong, Dept Stat & Actuarial Sci, Lung Fu Shan, Pokfulam Rd, Hong Kong, Peoples R China
3.Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Hubei, Peoples R China
4.Hang Seng Univ Hong Kong, Sch Decis Sci, Dept Math & Stat, Shatin,Siu Lek Yuen, Hong Kong, Peoples R China

Tian, Guo-Liang,Ding, Xiqian,Liu, Yin,et al. Some new statistical methods for a class of zero-truncated discrete distributions with applications[J]. COMPUTATIONAL STATISTICS,2019,34(3):1393-1426.

Tian, Guo-Liang,Ding, Xiqian,Liu, Yin,&Tang, Man-Lai.(2019).Some new statistical methods for a class of zero-truncated discrete distributions with applications.COMPUTATIONAL STATISTICS,34(3),1393-1426.

Tian, Guo-Liang,et al."Some new statistical methods for a class of zero-truncated discrete distributions with applications".COMPUTATIONAL STATISTICS 34.3(2019):1393-1426.