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 () 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.