The Annals of Probability

Ordering of Distributions and Rearrangement of Functions

Ludger Ruschendorf

Abstract

Some characterizations of semiorders defined on the set of all probability measures on $R^n$ by the set of Schur-convex functions and by some subsets of all convex functions are proved. A connection of these results to the theorem of Hardy, Littlewood and Polya on the rearrangement of functions is discussed. Furthermore, by means of the results on the ordering of probability measures a generalization of a theorem on doubly stochastic linear operators due to Ryff is proved.

Article information

Source
Ann. Probab., Volume 9, Number 2 (1981), 276-283.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994468

Digital Object Identifier
doi:10.1214/aop/1176994468

Mathematical Reviews number (MathSciNet)
MR606989

Zentralblatt MATH identifier
0461.60026

JSTOR