Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fr e ´ chet–Hoeffding upper bound

Abstract

Please cite this article as: I. Montes, S. Montes, Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fréchet-Hoeffding upper bound, Journal of Multivariate Analysis (2015), http://dx. AbstractStochastic dominance and statistical preference are stochastic orders with different interpretations: the former is based on the comparison of the marginal distributions while the latter is based on the joint distribution. Sklar's Theorem allows expressing the joint distribution in terms of the marginals by means of a copula. This paper investigates the relationship between these two stochastic orders for comonotone random variables and random variables coupled by an Archimedean copula.

Multivariate winning probabilities

“…In this vein, some of the present authors have proved that statistical preference is closer to another location parameter, namely the median [11]. We have also proved that, under common conditions such as independence, (first degree) stochastic dominance implies statistical preference [12,13,14,15], and that both concepts are equivalent in some particular situations, such as when comparing normally distributed random variables with the same variance [16].…”

“…Therefore, as we did in [14] for statistical preference, we aim to extend the connection between first degree stochastic dominance and probabilistic preference given in Theorem 17 for some prominent dependence models.…”

On optimal operational sequence of components in a warm standby system

“…In fact, it was even suggested in [7] to call it (at least at some instances) the stress-strength order, which naturally compares two random variables as in structural reliability. For recent advances, see [12] and [15]. Further, to avoid any confusion caused by the different definitions of the stochastic precedence order (see [3]), and as we are considering lifetimes of engineering items, we assume that the corresponding distribution functions are absolutely continuous.…”

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

“…in a suitable stochastic sense. For all mentioned basic stochastic orders (1.1) is transitive meaning that T i ≤ T j , for all 1 ≤ i < j ≤ n. We now define the stochastic precedence (SP) order (see, e.g., Boland et al [4], Finkelstein [5], Montes and Montes [8], to name a few). Definition 1.2 Let T 1 and T 2 be two nonnegative independent random variables.…”

“…We now define the stochastic precedence (SP) order that was not so extensively studied and applied as the foregoing orders (see [1,4,[7][8][9]12]). Definition 1.2: Let T 1 and T 2 be two independent random variables.…”