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Inferential properties with a novel two parameter Poisson generalized Lindley distribution with regression and

M R Irshad1, Veena D'cruz1, R Maya2

  • 1Department of Statistics, Cochin University of Science and Technology, Cochin, Kerala, India.

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|January 20, 2023
PubMed
Summary

A novel two-parameter Poisson generalized Lindley (TPPGL) distribution is introduced, offering enhanced mathematical properties and parameter estimation. This new statistical model demonstrates empirical importance through applications in regression and time series analysis.

Keywords:
Generalized Lindley distributionINAR(1) processcompoundingcount regression modelmaximum likelihood estimationmomentsover-dispersionsimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Mathematical Modeling

Background:

  • The Poisson distribution is a fundamental tool in probability.
  • The generalized Lindley distribution offers flexibility in modeling count data.
  • There is a need for new compound distributions with improved mathematical properties.

Purpose of the Study:

  • To propose a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution.
  • To systematically explore the mathematical properties of the TPPGL distribution.
  • To demonstrate the utility of the TPPGL distribution in count regression and time series models.

Main Methods:

  • Developing a new compound distribution by combining Poisson and generalized Lindley distributions.
  • Deriving closed-form expressions for key mathematical properties (e.g., probability generating function, moments).
  • Employing maximum likelihood estimation for parameter estimation, validated by Monte Carlo simulations.

Main Results:

  • The proposed TPPGL distribution exhibits desirable mathematical properties.
  • Parameter estimation via the likelihood-based method proved effective.
  • The TPPGL distribution successfully modeled real-world count data in regression and autoregressive processes.

Conclusions:

  • The novel TPPGL distribution provides a valuable addition to the field of statistical modeling for count data.
  • The TPPGL distribution demonstrates practical applicability in various statistical analyses.
  • The proposed compound distribution offers a flexible and robust alternative for count data analysis.