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Estimation of R3 = Pr(Y3 > max(Y1, Y2)) for Exponential Distribution

Piyali Kundu
2017 Journal of Advanced Statistics  
This paper deals with the estimation of the reliability function R3 = Pr(Y3 > max(Y1, Y2)), when the random variables Y1, Y2 and Y3 are independent exponential with respective unknown location parameters µ1, µ2 and µ3. Here we have derived several estimators of R3 which includes uniformly minimum variance unbiased estimator (UMVUE), Bayes estimator (BE) and generalized Bayes estimator(GBE). Moreover, we have compared these estimators based on their risks under different loss functions. Let Y i1
more » ... functions. Let Y i1 , Y i2 , · · · , Y ini be a random sample of size n i from the population of Y i . Define Throughout this section, these random samples will be used to estimate R 3 . Maximum Likelihood Estimator of R 3 It is well known that the MLEs of µ 1 , µ 2 and µ 3 , are µ 1M , µ 2M and µ 3M , respectively, where µ iM = Y i(1) , i = 1, 2, 3. Then from (3), MLE of R 3 will be given by
doi:10.22606/jas.2017.21006 fatcat:sqhkba43cjfknp3llg55whcuj4