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Estimation of \(P(Y < X)\) for Weibull distribution under progressive type-II censoring. (English) Zbl 1282.65017
Summary: Based on progressively Type II censored samples, we consider the estimation of \(R=P(Y<X)\) when \(X\) and \(Y\) are two independent Weibull distributions with different shape parameters, but having the same scale parameter. The maximum likelihood estimator, approximate maximum likelihood estimator, and Bayes estimator of \(R\) are obtained. Based on the asymptotic distribution of \(R\), the confidence interval of \(R\) are obtained. Two bootstrap confidence intervals are also proposed. Analysis of a real data set is given for illustrative purposes. Monte Carlo simulations are also performed to compare the different proposed methods.

MSC:
65C05 Monte Carlo methods
62C10 Bayesian problems; characterization of Bayes procedures
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