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On the Conway-Maxwell-Poisson point process

Author

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  • Ian Flint
  • Yan Wang
  • Aihua Xia

Abstract

The Poisson point process plays a pivotal role in modeling spatial point patterns. One of its key features is that the variance and the mean of the total number of points in a given region are equal, making it unsuitable for modeling point patterns that exhibit significantly different mean and variance. To tackle such point patterns, we introduce the class of Conway-Maxwell-Poisson point processes. Our model can easily be fitted with a logistic regression, its point counts in different regions are correlated and its log-likelihood in any subregion can be easily extracted. Both simulations and real data analyses have been carried out to demonstrate the performance of the proposed model.

Suggested Citation

  • Ian Flint & Yan Wang & Aihua Xia, 2024. "On the Conway-Maxwell-Poisson point process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(16), pages 5687-5705, August.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:16:p:5687-5705
    DOI: 10.1080/03610926.2023.2229028
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