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

Marko Obradović; Milan Jovanović; Bojana Milošević; Vesna Jevremović

Research Article

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

Year 2015, Volume: 44 Issue: 4, 949 - 964, 01.08.2015

Marko Obradović Milan Jovanović Bojana Milošević , Vesna Jevremović

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

References

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Year 2015, Volume: 44 Issue: 4, 949 - 964, 01.08.2015

Marko Obradović Milan Jovanović Bojana Milošević , Vesna Jevremović

Abstract

References

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There are 1 citations in total.

Details

Primary Language	English
Subjects	Statistics
Journal Section	Research Article
Authors	Marko Obradović This is me Milan Jovanović This is me Bojana Milošević Vesna Jevremović This is me
Publication Date	August 1, 2015
Published in Issue	Year 2015 Volume: 44 Issue: 4

Cite

APA	Obradović M., Jovanović M., Milošević B., & Jevremović V. (2015). Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics, 44(4), 949-964. https://izlik.org/JA36ZN76NU
AMA	1.Obradović M, Jovanović M, Milošević B, Jevremović V. Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics. 2015;44(4):949-964. https://izlik.org/JA36ZN76NU
Chicago	Obradović Marko, Jovanović Milan, Milošević Bojana, and Jevremović Vesna. 2015. “Estimation of P{X ≤ Y} for Geometric-Poisson Model”. Hacettepe Journal of Mathematics and Statistics 44 (4): 949-64. https://izlik.org/JA36ZN76NU.
EndNote	Obradović M, Jovanović M, Milošević B, Jevremović V (August 1, 2015) Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics 44 4 949–964.
IEEE	[1]Obradović M., Jovanović M., Milošević B., and Jevremović V., “Estimation of P{X ≤ Y} for geometric-Poisson model”, Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 4, pp. 949–964, Aug. 2015, [Online]. Available: https://izlik.org/JA36ZN76NU
ISNAD	Obradović Marko - Jovanović Milan - Milošević Bojana - Jevremović Vesna. “Estimation of P{X ≤ Y} for Geometric-Poisson Model”. Hacettepe Journal of Mathematics and Statistics 44/4 (August 1, 2015): 949-964. https://izlik.org/JA36ZN76NU.
JAMA	1.Obradović M, Jovanović M, Milošević B, Jevremović V. Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics. 2015;44:949–964.
MLA	Obradović Marko, et al. “Estimation of P{X ≤ Y} for Geometric-Poisson Model”. Hacettepe Journal of Mathematics and Statistics, vol. 44, no. 4, Aug. 2015, pp. 949-64, https://izlik.org/JA36ZN76NU.
Vancouver	1.Obradović M, Jovanović M, Milošević B, Jevremović V. Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics [Internet]. 2015 Aug. 1;44(4):949-64. Available from: https://izlik.org/JA36ZN76NU