An asymptotic test for symmetry of random variables based on fuzzy tools

A new measure of skewness for real random variables is proposed in this paper. The measure is based on a fuzzy representation of real-valued random variables which can be used to characterize the distribution of the original variable through the expected value of the 'fuzzified' random variable. Inferential studies concerning the expected value of fuzzy random variables provide us with a tool to analyze the asymmetry degree from random samples. As a first step, we propose an asymptotic test of symmetry. We present some examples and simulations to illustrate the behaviour of the proposed test. © 2006 Springer