Isaac Scientific Publishing

Journal of Advanced Statistics

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

Download PDF (503.7 KB) PP. 44 - 53 Pub. Date: March 1, 2017

DOI: 10.22606/jas.2017.21006


  • Piyali Kundu*
    Department of Statistics, Visva Bharati University, Santiniketan, India


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, μ 2and 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.


Stress-strength reliability, UMVUE, Bayes estimator, generalized Bayes estimator.


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