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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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