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Finite mixtures of mean-parameterized Conway–Maxwell–Poisson models

Author

Listed:
  • Dongying Zhan

    (University of Kentucky)

  • Derek S. Young

    (University of Kentucky)

Abstract

For modeling count data, the Conway–Maxwell–Poisson (CMP) distribution is a popular generalization of the Poisson distribution due to its ability to characterize data over- or under-dispersion. While the classic parameterization of the CMP has been well-studied, its main drawback is that it is does not directly model the mean of the counts. This is mitigated by using a mean-parameterized version of the CMP distribution. In this work, we are concerned with the setting where count data may be comprised of subpopulations, each possibly having varying degrees of data dispersion. Thus, we propose a finite mixture of mean-parameterized CMP distributions. An EM algorithm is constructed to perform maximum likelihood estimation of the model, while bootstrapping is employed to obtain estimated standard errors. A simulation study is used to demonstrate the flexibility of the proposed mixture model relative to mixtures of Poissons and mixtures of negative binomials. An analysis of dog mortality data is presented.

Suggested Citation

  • Dongying Zhan & Derek S. Young, 2024. "Finite mixtures of mean-parameterized Conway–Maxwell–Poisson models," Statistical Papers, Springer, vol. 65(3), pages 1469-1492, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01452-x
    DOI: 10.1007/s00362-023-01452-x
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