Estimation of $$P(X>Y)$$ P ( X > Y ) for Weibull distribution based on hybrid censored samples

Abstract

A Hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. Based on hybrid censored samples, this paper deals with the in- ference on R = P(X > Y ), when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape pa- rameter. The maximum likelihood estimator (MLE), and the approximate MLE (AMLE) of R are obtained. The asymptotic distribution of the maxi- mum likelihood estimator of R is obtained. Based on the asymptotic distribu- tion, the confidence interval of R can be derived. Two bootstrap confidence intervals are also proposed. We consider the Bayesian estimate of R, and propose the corresponding credible interval for R. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a real data set has also been presented for illustrative purposes.