Three-Dimensional Polynomial Copula and Stochastic Nontransitivity

Abstract As part of the author’s series of works, the phenomenon of stochastic nontransitivity for tuples of three random variables with a joint polynomial density of a special type on the unit cube is studied. It is shown when this density defines a copula and when there is nontransitivity. Maximization of the measure of nontransitivity is carried out.