Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data

Shin Zhu Sim; Ramesh C Gupta; Seng Huat Ong

doi:10.1515/ijb-2016-0070

Zero-inflated Conway-Maxwell Poisson Distribution to Analyze Discrete Data

Int J Biostat. 2018 Jan 9;14(1). doi: 10.1515/ijb-2016-0070.

Authors

Shin Zhu Sim¹, Ramesh C Gupta², Seng Huat Ong^{3

4}

Affiliations

¹ Department of Mathematical and Actuarial Sciences, Universiti Tunku Abdul Rahman, Kajang43000, Selangor, Malaysia.
² Department of Mathematics and Statistics, University of Maine, Orono, ME 04469-5752USA.
³ Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur50603, Malaysia.
⁴ Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Kuala Lumpur56000, Malaysia.

PMID: 29306919
DOI: 10.1515/ijb-2016-0070

Abstract

In this paper, we study the zero-inflated Conway-Maxwell Poisson (ZICMP) distribution and develop a regression model. Score and likelihood ratio tests are also implemented for testing the inflation/deflation parameter. Simulation studies are carried out to examine the performance of these tests. A data example is presented to illustrate the concepts. In this example, the proposed model is compared to the well-known zero-inflated Poisson (ZIP) and the zero- inflated generalized Poisson (ZIGP) regression models. It is shown that the fit by ZICMP is comparable or better than these models.

Keywords: Poisson; generalized Poisson; over and under-dispersion; regression; score and likelihood ratio tests; structural zeros; zero-inflation/deflation.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Biostatistics / methods*
Data Interpretation, Statistical*
Humans
Models, Statistical*
Poisson Distribution*