Estimation of P{X < Y} for geometric—exponential model based on complete and censored samples

ABSTRACT

This article deals with the estimation of R = P{X < Y}, where X and Y are independent random variables from geometric and exponential distribution, respectively. For complete samples, the MLE of R, its asymptotic distribution, and confidence interval based on it are obtained. The procedure for deriving bootstrap-p confidence interval is presented. The UMVUE of R and UMVUE of its variance are derived. The Bayes estimator of R is investigated and its Lindley's approximation is obtained. A simulation study is performed in order to compare these estimators. Finally, all point estimators for right censored sample from the exponential distribution, are obtained.

KEYWORDS:

• Bayes estimator
• Bootstrap confidence interval
• Censored data
• Exponential distribution
• Geometric distribution
• Lindley's approximation
• Maximum likelihood estimator
• Stress–strength
• Uniformly minimum variance unbiased estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62F12
• 62F15
• 62F40
• 62N01
• 62N05

Acknowledgement

The author would like to thank the anonymous referees for their useful comments and suggestions that improved the article.