Abstract
In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its variance are derived and also the Bayes estimator of R for conjugate prior distributions is obtained. Finally, we perform a simulation study in order to compare these estimators. keywords: stress-strength, geometric distribution, Poisson distribution, maximum likelihood estimator, Bayes estimator, UMVUE, bootstrap confidence intervals. MSC(2010): 62F10, 62F12, 62F15, 62F25, 62F40.
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