Testing equality of quantiles for several logistic populations with some real-life applications

Abstract

One of the novel methods described by the researchers for comparing several independent populations is to compare their quantiles. Researchers have previously considered comparing quantiles for normal and exponential model setups. In some cases, the datasets could be modeled using a different distribution, such as a logistic distribution. In this study, we consider the problem of comparing the quantiles for several ($k\ge 2$) logistic populations. First, the conventional likelihood ratio test is applied, and based on its asymptotic property, the cutoff point is determined. We propose two modifications of the likelihood ratio test- a standardized likelihood ratio test and a parametric bootstrap likelihood ratio test. Further, we propose a computational approach test to test the equality of quantiles by leveraging technology. The sizes and powers of all proposed tests are compared using an extensive simulation study. Except for the asymptotic likelihood ratio test, all the tests achieve the nominal level which has been revealed from our simulation study. Finally, we illustrate the importance of our model problem using two real-life situations.

Keywords:

• Asymptotic likelihood ratio test
• Computational approach test
• Parametric bootstrap likelihood ratio test
• Power
• Simulation study
• Size

Acknowledgments

The authors would like to sincerely express their thanks to the two anonymous reviewers and an Associate Editor for their constructive suggestions and comments which have helped significantly in improving the manuscript. The Second author (Manas Ranjan Tripathy) would like to thank the Science and Engineering Research Board (SERB), [EMR/2017/003078 dated 30th May 2018], Department of Science and Technology (DST), New Delhi, India, for providing some financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.