Likelihood-based methods for the zero-one-two inflated Poisson model with applications to biomedicine. Issue 6 (13th April 2023)

• Record Type: Journal Article
• Authors: Sun, Yuan; Zhao, Shishun; Tian, Guo-Liang; Tang, Man-Lai; Li, Tao
• Is Part Of: Journal of statistical computation and simulation. Volume 93:Issue 6(2023)
• Page Start: 956
• Page End: 982
• Publication Date: 2023-04-13
• Subjects: Bootstrap confidence intervals -- EM algorithm -- Fisher scoring algorithm -- zero-and-one-inflated Poisson model -- zero-one-two-inflated Poisson distribution; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2021.1970162
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: 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.