Likelihood-based methods for the zero-one-two inflated Poisson model with applications to biomedicine

Y Sun, S. S. Zhao, Guo-Liang Tian, Man Lai Tang, T. Li

Research output: Contribution to journalArticlepeer-review


To model count data with excess zeros, ones and twos, for the first time we introduce a so-called zero-one-two-inflated Poisson (ZOTIP) distribution, including the zero-inflated Poisson (ZIP) and the zero-and-one-inflated Poisson (ZOIP) distributions as two special cases. We establish three equivalent stochastic representations for the ZOTIP random variable to develop important distributional properties of the ZOTIP distribution. The Fisher scoring and expectation–maximization (EM) algorithms are derived to obtain the maximum likelihood estimates of parameters of interest. Bootstrap confidence intervals are also provided. Testing hypotheses are considered, simulation studies are conducted, and two real data sets are used to illustrate the proposed methods.
Original languageEnglish
Pages (from-to)956 - 982
Number of pages27
JournalJournal of Statistical Computation and Simulation
Issue number6
Early online date5 Sept 2021
Publication statusPublished - 2023


  • Bootstrap confidence intervals
  • EM algorithm
  • Fisher scoring algorithm
  • zero-and-one-inflated Poisson model
  • zero-one-two-inflated Poisson distribution


Dive into the research topics of 'Likelihood-based methods for the zero-one-two inflated Poisson model with applications to biomedicine'. Together they form a unique fingerprint.

Cite this