Applied Mathematics & Information Sciences

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The point at issue of this paper is to deliberate point and interval estimations of the stress - strength function, R. The maximum likelihood, Bayes, and parametric bootstrap estimators are obtained as point estimations of R. Based on the maximum likelihood estimate (MLE) of R, the distribution of R is determined and hence its confidence interval (CI) is estimated. The variance of ˆ R has been got in a closed form. Furthermore, four bootstrap CIs of R have been obtained. The results of Bayes estimation are computed under the squared error loss (SEL) and the LINEX loss functions. The acceptance rejection principle algorithm is applied to obtain the credible CI of R. Finally, two explanatory examples are introduced to explicate the precision of the obtained estimators .

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