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Weighted negative binomial distribution: properties and applications.

C Satheesh Kumar1, Prince Sathyan1

  • 1Department of Statistics, University of Kerala, Thiruvananthapuram, India.

Journal of Applied Statistics
|December 10, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a weighted negative binomial distribution, demonstrating its effectiveness in modeling COVID-19 data. The research details its statistical properties and parameter estimation methods.

Keywords:
Count data modelingMCMC simulationmaximum likelihood estimationmodel selectionnegative binomial distributionsurvival function

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • The negative binomial distribution is a common tool for count data analysis.
  • Existing models may not adequately capture the complexities of infectious disease spread, such as COVID-19.
  • A need exists for flexible statistical distributions to model epidemiological data.

Purpose of the Study:

  • To introduce and analyze a weighted negative binomial distribution.
  • To demonstrate the utility of this distribution in fitting COVID-19 datasets.
  • To derive key statistical properties and parameter estimation techniques for the proposed model.

Main Methods:

  • Derivation of the probability generating function, cumulative distribution function, survival, and hazard rate functions.
  • Formulation of expressions for factorial and raw moments and recurrence relations for probabilities.
  • Parameter estimation using the method of maximum likelihood and development of hypothesis testing procedures.
  • A simulation study to evaluate the performance of the parameter estimators.

Main Results:

  • The weighted negative binomial distribution provides a good fit for COVID-19 data.
  • Key statistical properties and moments of the distribution were derived.
  • Maximum likelihood estimation and hypothesis testing methods were developed and assessed via simulation.
  • The simulation study confirmed the performance of the parameter estimators.

Conclusions:

  • The weighted negative binomial distribution is a valuable and flexible tool for analyzing count data, particularly in epidemiological contexts like COVID-19.
  • The derived properties and estimation methods provide a solid foundation for its application.
  • This model offers an improved approach for understanding and predicting disease transmission patterns.