A Novel Bivariate Generalized Weibull Distribution with Properties and Applications

TL;DR

This paper introduces a new bivariate generalized Weibull distribution with derived properties, dependence measures, and applications, supported by estimation methods, simulations, and real data analysis.

Contribution

It presents a novel bivariate Weibull family with explicit properties, dependence measures, and estimation techniques, expanding the modeling tools in reliability analysis.

Findings

Derived explicit statistical properties and dependence measures.

Demonstrated effectiveness through simulations and real data.

Validated the distribution's applicability in real-life scenarios.

Abstract

Univariate Weibull distribution is a well-known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with ageing properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations