Generalization of the Pairwise Stochastic Precedence Order to the Sequence of Random Variables

Abstract

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the stochastic precedence order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

Construction of aggregation paradoxes through load-sharing models

“…In the last few years, in particular, it has attracted interest for different aspects and in different applied contexts; see e.g. the references [2], [6], [8], [13], and [23]. The same concept is also related to a comparison of statistical preference; see e.g.…”