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Bivariate Discrete Poisson-Lindley Distributions.

H Papageorgiou1, Maria Vardaki2

  • 1Department of Mathematics, National and Kapodistrian University of Athens, Athens, Greece.

Journal of Statistical Theory and Practice
|May 2, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces two new families of bivariate discrete Poisson-Lindley distributions, offering flexible models for analyzing dependent count data. These distributions are characterized by a small number of parameters and over-dispersed marginals, making them suitable for various applications.

Keywords:
Poisson mixturesPoisson–Lindley distributiongeneralized binomial

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Area of Science:

  • Statistics
  • Probability Theory
  • Statistical Distributions

Background:

  • Bivariate discrete distributions are essential for modeling paired count data.
  • Existing models may lack flexibility or have complex parameter estimation.
  • The Poisson-Lindley distribution offers desirable properties for count data modeling.

Purpose of the Study:

  • To introduce two novel families of bivariate discrete Poisson-Lindley distributions.
  • To provide flexible and parsimonious statistical models for bivariate dependent count data.
  • To derive key distributional properties and facilitate parameter estimation.

Main Methods:

  • Construction of bivariate distributions by mixing parameters or generalizing existing models.
  • Utilizing probability-generating functions to derive general and specific properties.
  • Derivation of expressions for probabilities, moments, conditional distributions, and regression functions.

Main Results:

  • Two families of bivariate discrete Poisson-Lindley distributions were successfully derived.
  • Models possess attractive properties, including few parameters (two or three) and easily estimable parameters.
  • Marginal distributions exhibit over-dispersion, suitable for real-world count data.

Conclusions:

  • The proposed bivariate Poisson-Lindley distributions offer a promising framework for analyzing bivariate dependent count data.
  • Their parsimony and desirable statistical properties suggest broad applicability across various scientific and applied fields.
  • These distributions provide a valuable addition to the toolkit for statistical modeling of count data.