TY - JOUR
T1 - Likelihood-based methods for the zero-one-two inflated Poisson model with applications to biomedicine
AU - Sun, Y
AU - Zhao, S. S.
AU - Tian, Guo-Liang
AU - Tang, Man Lai
AU - Li, T.
N1 - © 2021 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021/9/5
Y1 - 2021/9/5
N2 - 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.
AB - 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.
KW - Bootstrap confidence intervals
KW - EM algorithm
KW - Fisher scoring algorithm
KW - zero-and-one-inflated Poisson model
KW - zero-one-two-inflated Poisson distribution
UR - http://www.scopus.com/inward/record.url?scp=85114417529&partnerID=8YFLogxK
U2 - 10.1080/00949655.2021.1970162
DO - 10.1080/00949655.2021.1970162
M3 - Article
VL - 93
SP - 956
EP - 982
JO - Journal of Statistical Computation and Simulation
JF - Journal of Statistical Computation and Simulation
IS - 6
ER -