- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 4
- Estimation of P{X ≤ Y} for geometric-Poisson model
Estimation of P{X ≤ Y} for geometric-Poisson model
Authors : Marko Obradović, Milan Jovanović, Bojana Milošević, Vesna Jevremović
Pages : 949-964
View : 13 | Download : 5
Publication Date : 2015-08-01
Article Type : Research
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