Fuzzy representations of real-valued random variables: applications to exploratory and inferential studies

The so-called fuzzy representations of real-valued random variables are reviewed. They are used to visualize or/and characterize distributions through fuzzy sets. Various fuzzy representations useful to explore or test about different characteristics of real distributions are described. The main developments concerning the representation, goodness-of-fit, equality of distribution and asymmetry are overviewed. New inferential strategies for the equality of two-paired distributions based on bootstrap techniques are introduced. They are analyzed theoretically and empirically. Copyright Sapienza Università di Roma 2013