search for




 

Likelihood-based inference for the ratio of shape parameters of generalized exponential distributions
Journal of the Korean Data & Information Science Society 2018;29:795-806
Published online May 31, 2018
© 2018 Korean Data and Information Science Society.

Jaeun Lee1 · Woo Dong Lee2 · Sang Gil Kang3

1Department of Mathematics, Yeungnam University
2Division of Cosmetic Science and Technology, Daegu Haany University
3Department of Computer and Data Information, Sangji University
Correspondence to: Professor, Department of Computer and Data Information, Sangji University, Wonju 220-702, Korea. E-mail: sgkang@sangji.ac.kr
Received March 30, 2018; Revised April 19, 2018; Accepted April 20, 2018.
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
This article deals with the likelihood-based inference for the ratio of the shape parameters of the generalized exponential distribution. When the parameter of interest is the ratio of the shape parameters, we develop the likelihood-based inference based on the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the parameter of interest. To show the performances of the proposed likelihood-based methods, we perform simulations and compare the two likelihood-based statistics when the sample size is small. An example based on simulated data is given. From the numerical results, we can see that the modified signed log-likelihood ratio statistic has good performances in terms of coverage probabilities of confidence intervals and power, and gives desirable results even with a small sample size.
Keywords : Generalized exponential distribution, likelihood-based inference, modified signed log-likelihood ratio, ratio of the shape parameters, signed log-likelihood ratio.