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Inference of \(R=P(Y<X)\) for two-parameter Rayleigh distribution based on progressively censored samples. (English) Zbl 1440.62353
Summary: The UMVUE and maximum likelihood estimator of \(R=P(Y<X)\) for independent progressively Type-II censored samples from two-parameter Rayleigh distributions with different scale parameters are derived. Also the exact, asymptotic and bootstrap confidence intervals for \(R\) are evaluated. Using Gibbs sampling, the Bayes estimates and corresponding credible intervals for \(R\) are obtained. Applying Monte Carlo simulations, we compare the performances of the different estimation methods. Finally we use of two real data sets and show the competitive performance of the presented methods.

MSC:
62N02 Estimation in survival analysis and censored data
62F10 Point estimation
62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions
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