Statistical inference on quantiles of two independent populations under uncertainty

Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a specific significance level to decide whether the underlying fuzzy null hypothesis can be rejected or not. The effectiveness of the proposed two-sample test on quantiles is investigated via numerical examples.