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The zero-and-plus/minus-one inflated extended-Poisson distribution.

Maher Kachour1, Christophe Chesneau2

  • 1ESSCA School of Management, Lyon, France.

Journal of Applied Statistics
|September 9, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a novel count data distribution, extending the zero-and-one-inflated Poisson model. The new distribution effectively handles excess zeros, ones, and minus ones in datasets like football scores.

Keywords:
Zero-and-one-inflated Poisson distributioncount data analysisdiscrete distribution defined onextended Poisson distributionsimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Econometrics

Background:

  • Count data frequently exhibit excess zeros or ones, posing challenges for standard Poisson models.
  • Existing zero-inflated and one-inflated models may not adequately capture data with both excess zeros and ones, or negative counts.

Purpose of the Study:

  • Introduce a new flexible distribution for count data, termed the "[Distribution Name]" distribution.
  • Extend the capabilities of existing zero-and-one-inflated Poisson distributions.
  • Provide a robust statistical tool for analyzing count data with complex zero/one inflation patterns.

Main Methods:

  • Define the novel [Distribution Name] distribution and derive its key probabilistic properties.
  • Investigate methods for parameter estimation within the proposed distribution framework.
  • Conduct simulation studies to evaluate the performance and accuracy of the estimation techniques.

Main Results:

  • The proposed [Distribution Name] distribution demonstrates flexibility in modeling count data with excess zeros, ones, and minus ones.
  • Parameter estimation methods are shown to be effective through simulation experiments.
  • The distribution's practical utility is validated using a real-world dataset of football scores.

Conclusions:

  • The [Distribution Name] distribution offers a valuable alternative for analyzing specialized count data.
  • The developed estimation techniques provide reliable parameter estimates for the new distribution.
  • This work contributes a new tool for statistical modeling in fields with excess zero/one-inflated count data.