# Journal of Advanced Statistics

### Estimation of* R*_{3} = Pr(*Y*_{3} > max(*Y*_{1}, Y_{2})) for Exponential Distribution

_{3}

_{1}, Y

_{2}

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

### Author(s)

**Piyali Kundu**^{*}

Department of Statistics, Visva Bharati University, Santiniketan, India

### Abstract

*R*= Pr(

_{3}*Y*> max(

_{3}*Y*)), when the random variables

_{1}, Y_{2}*Y*,

_{1}*Y*and

_{2}*Y*are independent exponential with respective unknown location parameters

_{3}*μ*

_{1},

*μ*

_{ 2}and

*μ*

_{3}. Here we have derived several estimators of

*R*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.

_{3}### Keywords

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