On the theory of high convexity stochastic orders (Q1976511)

The aim of this article is two-fold: (1) In Section 2 there is derived a simple but general condition under which two \(s\)-convex ordered random variables must be stochastically equal, and the usefulness in statistics of this result is explained. (2) Section 3 analyzes the computational relationship between the canonical moments and the extremal distributons in the \(s\)-convex sense. The paper shows that the \(s\)th moments of the extremal distributions can be obtained in an algebraic manner using the theory of \(s\)-convex stochastic orders.