New Bivariate Pareto Type II Models.

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The Pareto Type II distribution is crucial in reliability modeling and lifetime testing.
• Bivariate distributions are essential for analyzing dependent lifetime data.
• Existing bivariate Pareto models may have limitations in capturing complex dependencies.

Purpose of the Study:

• To introduce two new bivariate Pareto Type II distributions.
• To explore methods for parameter estimation and performance evaluation.
• To demonstrate the practical applicability of the proposed distributions.

Main Methods:

• Development of bivariate Pareto Type II distributions using copula functions.
• Incorporation of mixture and copula approaches for a second distribution.
• Parameter estimation via the maximum likelihood method.
• Performance assessment through simulation studies.

Main Results:

• Successful derivation of two distinct bivariate Pareto Type II distributions.
• Demonstration of parameter estimation accuracy through simulations.
• Evidence of the proposed distributions' flexibility in fitting real-world data.

Conclusions:

• The proposed bivariate Pareto Type II distributions offer valuable tools for reliability and lifetime analysis.
• The methods employed provide a robust framework for developing and analyzing complex bivariate distributions.
• The distributions are suitable for modeling dependent data in various real-life scenarios.