IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v34y2019i3d10.1007_s00180-018-00860-0.html
   My bibliography  Save this article

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

Author

Listed:
  • 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

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 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.

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-00860-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-00860-0. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Mallaigh Nolan). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.