A Fuzzy Approach to Stochastic Dominance of Random Variables

Abstract

The discrete dice model essentially amounts to comparing discrete uniform probability distributions and generates reciprocal relations that exhibit a particular type of transitivity called dice-transitivity. In this contribution, this comparison method is extended and applied to general probability distributions and the generated reciprocal relations are shown to generalize the concept of stochastic dominance. For a variety of parametrized probability distributions, we analyse the transitivity properties of these reciprocal relations within the framework of cycletransitivity. The relationship between normal probability distributions and the different types of stochastic transitivity is emphasized.