Estimation of P{X ≤ Y} for geometric-Poisson model

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Hacettepe Journal of Mathematics and Statistics
Volume:44 Issue:4
Estimation of P{X ≤ Y} for geometric-Poisson model

Estimation of P{X ≤ Y} for geometric-Poisson model

Authors : Marko OBRADOVİĆ, Milan JOVANOVİĆ, Bojana MİLOŠEVİĆ, Vesna JEVREMOVİĆ

Pages : 949-964

View : 37 | Download : 10

Publication Date : 2015-08-01

Article Type : Research Paper

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, maxi mum likelihood estimator, Bayes estimator, UMVUE, bootstrap confidence inter vals

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