Stress–Strength Parameter Estimation Based on Type-II Hybrid Progressive Censored Samples for a Kumaraswamy Distribution

Abstract

In this paper, when the stress and strength are two independent Kumaraswamy random variables, we derive the point and interval estimate of the stress-strength parameter, from both frequentist and Bayesian viewpoints, under the Type-II hybrid progressive censoring scheme. In fact, the problem is solved in two cases. First, with the assumption that the stress and strength have different first shape parameters and the common second shape parameter, we attain maximum likelihood estimate (MLE), approximation MLE, and two Bayesian approximation estimates, Lindley's approximation and the Markov chain Monte Carlo (MCMC) method, due to lack of closed forms. Also, the asymptotic confidence interval of R is constructed by asymptotic distribution of it. Moreover, by using the MCMC method, we achieve the highest posterior density credible intervals. Second, with the assumption that the common shape parameter is known, we attain the MLE, the exact Bayes estimate, and the uniformly minimum-variance unbiased estimate of R. Also, we construct the asymptotic and Bayesian intervals for the stress-strength parameter. Furthermore, to compare the performance of various methods, we apply the Monte Carlo simulation. Finally, one real dataset is analyzed for demonstrative aims.