Estimation of R = P(Y < X) using k-Upper Record Values from Kumaraswamy Distribution

Authors

Naser A. Abou-Elheggag, Mathematics Department, Faculty of science, Sohag University, Sohag 82524, EgyptFollow
Al-Wageh A. Farghal
Hanan A. Ramadan

Author Country (or Countries)

Egypt

Abstract

The problem of estimating the stress-strength R = P(Y < X) when X and Y are two independent ordinary samples was considered by many authors. In this paper, the problem of estimation of R = P(Y < X) when X and Y are two independent k-upper record values from the Kumaraswamy distribution is considered. Maximum likelihood (ML) and Bayes techniques are used for this purpose. The maximum likelihood estimator is used to construct both an exact confidence interval and percentile bootstrap confidence interval of the stress-strength. Bayes estimators have been developed under both symmetric (squared error) and asymmetric (LINEX) loss functions. Monte Carlo simulations are performed to compare the performances of the different methods.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/070204

Recommended Citation

A. Abou-Elheggag, Naser; A. Farghal, Al-Wageh; and A. Ramadan, Hanan (2018) "Estimation of R = P(Y < X) using k-Upper Record Values from Kumaraswamy Distribution," Journal of Statistics Applications & Probability: Vol. 7: Iss. 2, Article 4.
DOI: http://dx.doi.org/10.18576/jsap/070204
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol7/iss2/4