Stochastic ordering for permutation symmetric distributions

Marco Scarsini (1, 2) , Moshe Shaked (3)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali
3 University of Arizona

In this paper the meaning of the stochastic ordering relation is studied when the random vectors which are compared are assumed to be permutation symmetric. It is shown that in order to establish the stochastic ordering relation between two such random vectors it is enough to consider only upper sets which are symmetric, rather than all upper sets. Further results for such bivariate random vectors are also given. Some comments regarding stochastic ordering of general random vectors and of vectors of order statistics are also included. Some applications are described.

Keywords: Probability law; Random vector; Permutation; Symmetry; Order statistics; Utility function; Reliability; Exchangeable processus

Domains: Economy and decision science

Marco Scarsini, Moshe Shaked. Stochastic ordering for permutation symmetric distributions. Statistics and Probability Letters, 1990, Vol. 9, N°3, pp. 217-222. ⟨hal-00542131⟩