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Small sample confidence intervals of the stress-strength reliability of inverse exponential distribution
Journal of the Korean Data & Information Science Society 2021;32:931-41
Published online September 30, 2021;  https://doi.org/10.7465/jkdi.2021.32.5.931
© 2021 Korean Data and Information Science Society.

Hong Kyung Pak1 · Sang Gil Kang2 · Woo Dong Lee3

1Department of Medical Information Technology and Data Science, Daegu Haany University
2Department of IT Statistics, Sangji University
3Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University
Correspondence to: 1 Professor, Department of Medical Information Technology and Data Science, Daegu Haany University, Kyungsan, 38610, Korea.
2 Professor, Department of IT Statistics, Sangji University, Wonju, 26339, Korea.
3 Professor, Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University, Kyungsan, 38610, Korea. E-mail: wdlee@dhu.ac.kr
Received July 9, 2021; Revised August 4, 2021; Accepted August 4, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, when the parameter of interest is the stress-strength reliability of inverse exponential distribution, the confidence interval estimation problem of the reliability is studied. Three confidence intervals are developed. The exact confidence interval based on the sampling distribution of the maximum likelihood estimator and two approximate confidence intervals based on the likelihood function are developed. Through the simulation study, these confidence intervals are compared with respect to the estimated coverage probability, the length and bilateral properties of confidence intervals. Data sets of lifetimes of electrical insulators observed under two different voltages are analyzed.
Keywords : Confidence interval, likelihood function, modified signed log-likelihood ratio statistic, signed log-likelihood ratio statistic.