Unlike the usual stochastic order, total positivity order is closed under conditioning. Here we provide a general formulation of the preservation properties of the order under conditioning; we study certain properties of the order including translation properties and the implications of having...

Let X = (X1, X2,..., Xn) be a random vector in Rn (Euclidean n-space) with density f(x). X or f(x) is said to be multivariate reverse rule of order 2 (MRR2) if f(x [curly logical or] y) f(x [curly logical and] y) = f(x) f(y) where the lattice operations x [curly logical and] y and x [curly...

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible...

Suppose you observe a finite sequence of random variables from some known joint distribution F, you can stop the process at any time and your profit is the last observed value. If an optimal stopping rule is used, denote the expected profit by VF. What kind of ordering on multivariate...

A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) = f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2...

In this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by...

It has been proved (Sklar, 1959, Publ. Inst. Statist. Univ. Paris 8 229-231) that any multivariate distribution function depends on its arguments only through its marginal distributions. An analogous result will be proved in the general framework of probability measures on (Polish) product...

Several well known integral stochastic orders (like the convex order, the supermodular order, etc.) can be defined in terms of the Hessian matrix of a class of functions. Here we consider a generic Hessian order, i.e., an integral stochastic order defined through a convex cone of Hessian...

In this paper we consider several multivariate extensions of comonotonicity. We show that naive extensions do not enjoy some of the main properties of the univariate concept. In order to have these properties, more structures are needed than in the univariate case.