In this work, we compare conditional distributions derived from bivariate archimedean copulas in terms of their respective variabilities using the dispersive stochastic order. Specifically, we fix the underlying copula and we consider the effect of increasing the second component on the...

This paper extends a useful property of the increasing convex order to the multivariate orthant convex order. Specifically, it is shown that vectors of sums of comonotonic random variables dominate in the orthant convex order vectors of sums of random variables that are smaller in the increasing...

In this work, we derive a sufficient condition for the orthant convex order based on the single crossing of the respective joint survival functions. This condition is expressed in terms of the generators for Archimedean copulas. Numerical examples show that this condition is valid for members of...

Several well-known stochastic orderings are defined in terms of iterated integrals of distribution or survival functions. In this note we will provide necessary conditions for some variability orderings of the above type. These conditions will be based on the comparison of mean differences,...

In many applications, common factors influence a set of failure (or survival) times of interest. This is, for instance, the case in mortality analysis, where mortality is influenced by socio-economic and health factors, or in the analysis of time-to-failure observations, where the items are...

The purpose of this note is two-fold. First we derive a simple condition under which two s-convex ordered random variables must be stochastically equal, and we indicate the potential usefulness of this result in statistics. Then we highlight the relationship between the canonical moments and the...

The purpose of this work is to provide upper bounds on the stop-loss and total variation distances between random sums. The main theoretical argument consists in defining discrete analogs of the classical ideal metrics considered by Rachev and Rüschendorf (Adv. Appl. Probab. 22 (1990) 350). An...