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


  • Guo-Liang Tian

    (Southern University of Science and Technology)

  • Xiqian Ding

    (The University of Hong Kong)

  • Yin Liu

    () (Zhongnan University of Economics and Law)

  • Man-Lai Tang

    (The Hang Seng University of Hong Kong)


Abstract 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 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.

Suggested Citation

  • Guo-Liang Tian & Xiqian Ding & Yin Liu & Man-Lai Tang, 2019. "Some new statistical methods for a class of zero-truncated discrete distributions with applications," Computational Statistics, Springer, vol. 34(3), pages 1393-1426, September.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-00860-0
    DOI: 10.1007/s00180-018-00860-0

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