Date of Original Version
6-1996
Type
Article
Published In
The Annals of Statistics, Vol. 24, No. 3 (Jun., 1996), pp. 1250-1264
Abstract or Table of Contents
Choquet capacities are a generalization of probability measures that arise in robustness, decision theory and game theory. Many capacities that arise in robustness are symmetric or can be transformed into symmetric capacities. We characterize the extreme points of the set of upper distribution functions corresponding to coherent, symmetric Choquet capacities on [0,1]. We also show that the set of 2-alternating capacities is a simplex and we give a Choquet representation of this set.