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Classic count models struggle with bidispersed data. This study introduces a Conway-Maxwell-Poisson model with a look-up method, making it practical for analyzing data with both under- and overdispersion.

Keywords:
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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Classic regression models like Poisson and negative binomial struggle with count data exhibiting both underdispersion and overdispersion.
  • The Conway-Maxwell-Poisson (CMP) distribution can model bidispersed data but is computationally challenging due to its normalizing constant.

Purpose of the Study:

  • To propose a computationally efficient method for analyzing bidispersed count data using the Conway-Maxwell-Poisson distribution.
  • To demonstrate the practicability of this method across various real-world datasets.

Main Methods:

  • Developed a look-up method involving pre-computation of the rate parameter for the Conway-Maxwell-Poisson distribution.
  • Validated the proposed method through a simulation study.
  • Applied the method to three diverse datasets: takeover bids, yellow cards in football, and cricket match data.

Main Results:

  • The look-up method significantly reduces computation time, making the CMP model a feasible alternative for bidispersed data.
  • The model successfully accommodated both under- and overdispersion in the analyzed datasets.
  • Demonstrated the method's applicability to small, medium, and large datasets.

Conclusions:

  • The proposed look-up method enhances the practical utility of the Conway-Maxwell-Poisson distribution for analyzing complex count data.
  • This approach provides a valuable tool for researchers dealing with bidispersed data in fields ranging from finance to sports analytics.