Bivariate Power Lindley Models Based on Copula Functions Under Type‐II Censored Samples With Applications in Industrial and Medical Data

This study introduces three innovative bivariate models to address complex dependencies between random variables in real‐world applications. Specifically, we develop bivariate power Lindley (BPL) distribution models utilizing the Gumbel, Frank, and Clayton copulas. These models effectively capture the underlying relationships between variables, particularly under a Type‐II censored sampling scheme. Parameter estimation is performed using both maximum likelihood and Bayesian methods, with asymptotic and credible confidence intervals computed. We also employ the Markov Chain Monte Carlo method for numerical analysis. The proposed methodology is demonstrated through the analysis of multiple datasets: the first investigates burr formation in manufacturing with two sets of observations, while the second and third datasets explore medical data on diabetic nephropathy and infection recurrence times in kidney patients, respectively. The results highlight the practical applicability and robustness of these newly proposed bivariate models.