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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we perform a simulation study in order to compare these estimators.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we estimate R=P{X≤Y} when X and Y are independent random variables from geometric and Poisson distribution respectively.
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Key Findings & Data:We find maximum likelihood estimator of R and its asymptotic distribution.
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Conclusion & Impact:Finally, we perform a simulation study in order to compare these estimators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:stress-strength · geometric distribution · Poisson distribution
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.
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Cite This Article
OBRADOVİĆ, M., JOVANOVİĆ, M., MİLOŠEVİĆ, B., JEVREMOVİĆ, V. (2022). Estimation of P{X ≤ Y} for geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 4, 949–964. https://ajindex.com/articles/530293