Inference on Stress-Strength Model for a Kumaraswamy Distribution Based on Hybrid Progressive Censored Sample

Abstract

In this paper, we obtain the point and interval estimates of the stress-strength parameter under the hybrid progressive censored scheme, when stress and strength are considered as two independent random variables of Kumaraswamy. We solve the problem in three cases as followings: First, assuming that stress and strength have different first shape parameters and the common second shape parameter, we obtain maximum likelihood estimation (MLE), approximation maximum likelihood estimation (AMLE) and two Bayesian approximation estimates due to the lack of explicit forms. Also, we construct the asymptotic and highest posterior density (HPD) intervals for R. Moreover, we consider the existence and uniqueness of the MLE. Second, assuming that common second shape parameter is identified, we derive the MLE and exact Bayes estimate of R. Third, assuming that all parameters are unknown and different, we achieve the statistical inference of R, namely MLE, AMLE and Bayesian inference of R. Furthermore, we apply the Monte Carlo simulations for comparing the performance of different methods. Finally, we analyze two data sets for illustrative purposes.