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On estimation of $$R=P(Y<X)$$ for exponential distribution under progressive type-II censoring. (English) Zbl 1431.62463
Summary: This paper deals with the estimation of the stress-strength parameter $$R=P(Y<X)$$, when $$X$$ and $$Y$$ are independent exponential random variables, and the data obtained from both distributions are progressively type-II censored. The uniformly minimum variance unbiased estimator and the maximum-likelihood estimator (MLE) are obtained for the stress-strength parameter. Based on the exact distribution of the MLE of $$R$$, an exact confidence interval of $$R$$ has been obtained. Bayes estimate of $$R$$ and the associated credible interval are also obtained under the assumption of independent inverse gamma priors. An extensive computer simulation is used to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose.

##### MSC:
 62N05 Reliability and life testing 62N02 Estimation in survival analysis and censored data 62F10 Point estimation 62F15 Bayesian inference 62F25 Parametric tolerance and confidence regions
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