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A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data.

B I Mohammed1,2, Nicholas Makumi3, Ramy Aldallal4

  • 1Department of Mathematics, Faculty of Science, Jeddah University, 2749 Asfan Rd. Jeddah 21589, Saudi Arabia.

Computational and Mathematical Methods in Medicine
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Summary

This study introduces the bivariate Poisson exponential-exponential conditional (BPEEC) distribution for medical data analysis. The BPEEC model offers a new tool for analyzing bivariate lifetime data, with parameter estimation and comparisons to existing models.

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Area of Science:

  • Medical Data Analysis
  • Probability Theory
  • Statistical Modeling

Background:

  • The bivariate Poisson exponential-exponential distribution is crucial for analyzing medical lifetime data.
  • Existing bivariate distributions may not fully capture the complexities of certain medical datasets.

Purpose of the Study:

  • To introduce and define the bivariate Poisson exponential-exponential conditional (BPEEC) distribution.
  • To derive key properties and estimation methods for the BPEEC model.
  • To compare the BPEEC model with other bivariate distributions using real-world medical data.

Main Methods:

  • Construction of the BPEEC distribution using conditional properties, probability mass function (pmf), and probability density function (pdf).
  • Derivation of normalized constants, conditional densities, regression functions, and product moments.
  • Application of maximum likelihood and pseudolikelihood estimation methods for BPEEC parameters.
  • Comparative analysis of BPEEC against bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) using real bivariate datasets.

Main Results:

  • The study successfully defines the BPEEC distribution and derives its fundamental properties.
  • Maximum likelihood and pseudolikelihood methods are demonstrated as effective for parameter estimation.
  • Empirical analysis shows the performance of the BPEEC model in real medical data scenarios.
  • Comparative results highlight the BPEEC model's potential advantages over BEC and BPEC in specific applications.

Conclusions:

  • The BPEEC distribution provides a valuable addition to the toolkit for bivariate lifetime data analysis in medical research.
  • The proposed estimation techniques are robust and suitable for practical application.
  • The BPEEC model demonstrates competitive or superior performance compared to existing bivariate distributions in analyzed medical datasets.