In an analogous way to the classical case of a probability measure, we extend the notion of an increasing convex (concave) stochastic dominance relation to the case of a normalised monotone (but not necessarily additive) set function also called a capacity. We give different characterizations of...

A great number of articles have dealt with stochastic comparisons of ordered random variables in the last decades. In particular, distributional and stochastic properties of ordinary order statistics have been studied extensively in the literature. Sequential order statistics are proposed as an...

By analogy with the classical case of a probability measure, we extend the notion of increasing convex (concave) stochastic dominance relation to the case of a normalized monotone (but not necessarily additive) set function also called a capacity. We give different characterizations of this...

There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F1 , F2 and stochastic orderings between their inverses F −1 , F −1. This underlies some theories of utility in the case of the cdf and deprivation indices in the case of the inverse....