On bivariate generalized lifetime distribution

Abstract

This paper introduces a new class of bivariate lifetime distributions whose marginals are exponentiated general lifetime distributions. This class includes a large number of two-dimensional lifetime models as submodels. Some important mathematical quantities such as joint density, conditional distributions, conditional moments, and quantile regression are obtained. Copula associated with the proposed model and some results related to copula-based extropy are also studied. The derived quantities are more crucial for improving the accuracy of predictions and estimates in real-world modeling. The methods of maximum likelihood and Bayesian estimation are considered to estimate the model parameters in a general way. Further, we conducted a simulation study to assess the performance of the derived estimators, observing their behavior based on the mean squared error criteria under different parameter combinations and sample sizes. Finally, we analyzed a bivariate medical dataset to demonstrate the effectiveness of the proposed distribution in real-world scenarios and assess its fit within the derived submodels of the bivariate lifetime distribution. The analysis of the real-data application indicates that the generalized bivariate Weibull distribution provides the best fit among the submodels of lifetime distributions. © 2025 Elsevier B.V., All rights reserved.