Bivariate power Lomax distribution with medical applications

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime data analysis often requires flexible bivariate distributions.
• Existing models may not fully capture the dependencies in bivariate lifetime data.
• The power Lomax distribution is a useful univariate model for reliability.

Purpose of the Study:

• To propose a novel bivariate power Lomax distribution using Farlie-Gumbel-Morgenstern (FGM) copulas.
• To investigate the statistical properties and reliability measures of the proposed bivariate distribution.
• To explore parameter estimation methods for the new model.

Main Methods:

• Development of the bivariate power Lomax distribution (BFGMPLx) via FGM copulas.
• Derivation and analysis of statistical properties: marginal and conditional distributions, moments, and dependence measures.
• Computation of reliability functions: survival, hazard rate, and mean residual life.
• Parameter estimation using Maximum Likelihood Estimation (MLE) and Bayesian approaches.
• Validation through Monte Carlo simulations and computation of confidence/credible intervals.

Main Results:

• The proposed BFGMPLx distribution is established, offering a flexible framework for bivariate lifetime data.
• Comprehensive analysis of its statistical and reliability characteristics, including dependence properties.
• Demonstration of effective parameter estimation via both MLE and Bayesian methods.
• Simulation studies confirm the performance of the estimators and the validity of the confidence intervals.

Conclusions:

• The BFGMPLx distribution provides a valuable addition to the toolkit for bivariate lifetime data modeling.
• The study successfully characterized its statistical and reliability properties.
• The proposed estimation techniques are robust and suitable for practical applications in reliability analysis.