Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression

Kimberly F. Sellers, Derek S. Young

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


While excess zeros are often thought to cause data over-dispersion (i.e. when the variance exceeds the mean), this implication is not absolute. One should instead consider a flexible class of distributions that can address data dispersion along with excess zeros. This work develops a zero-inflated sum-of-Conway-Maxwell-Poissons (ZISCMP) regression as a flexible analysis tool to model count data that express significant data dispersion and contain excess zeros. This class of models contains several special case zero-inflated regressions, including zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-inflated binomial (ZIB), and the zero-inflated Conway-Maxwell-Poisson (ZICMP). Through simulated and real data examples, we demonstrate class flexibility and usefulness. We further utilize it to analyze shark species data from Australia's Great Barrier Reef to assess the environmental impact of human action on the number of various species of sharks.

Original languageEnglish
Pages (from-to)1649-1673
Number of pages25
JournalJournal of Statistical Computation and Simulation
Issue number9
StatePublished - Jun 13 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Count data modelling
  • discrete data
  • over-dispersion
  • under-dispersion
  • zero-inflated Poisson
  • zero-inflated negative binomial

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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