Independent k-sample equality distribution test based on the fuzzy representation

Abstract

Classical tests for the equality of distributions of real-valued random variables are widely applied in Statistics. When the normality assumption for the variables fails, non-parametric techniques are to be considered; Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman tests, among other alternatives. Fuzzy representations of real-valued random variables have been recently shown to describe in an effective way the statistical behaviour of the variables. Indeed, the expected value of certain fuzzy representations fully characterizes the distribution of the variable. The aim of this paper is to use this characterization to test the equality of distribution for two or more real-valued random variables, as an alternative to classical procedures. The inferential problem is solved through a parametric test for the equality of expectations of fuzzy-valued random variables. Theoretical results on inferences for fuzzy random variables support the validity of the test. Besides, simulation studies and practical applications show the empirical goodness of the method.