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Likelihood-based inference for the ratio of the parameters of the inverse exponential distributions
Journal of the Korean Data & Information Science Society 2019;30:1399-408
Published online November 30, 2019;  https://doi.org/10.7465/jkdi.2019.30.6.1399
© 2019 Korean Data and Information Science Society.

Sang Gil Kang1 · Hong Kyung Pak2 · Woo Dong Lee3

1Department of Computer and Data Information, Sangji University
2Department of Medical Information Technology and Data Science, Daegu Haany University
3Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University
Correspondence to: Professor, Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University, Kyungsan 38610, Korea. E-mail: wdlee@dhu.ac.kr
Received August 8, 2019; Revised October 23, 2019; Accepted November 12, 2019.
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 article, two likelihood-based methods are developed to make a statistical inference of the ratio of the parameters of the inverse exponential distributions. The exact method and the likelihood-based methods under the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are developed. The confidence intervals of the ratio and the test of the ratio of the parameters of two independent inverse exponential distributions are studied by proposed statistics. For comparing the accuracy of the proposed methods, we investigate the coverage probability, the bilateral symmetry and length of the confidence intervals in the small sample size. Also, the power of the test statistics are compared. And a real data example is provided.
Keywords : Confidence interval, hypothesis testing, inverse exponential distribution, modified signed log-likelihood ratio statistic, signed log-likelihood ratio statistic.