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Multivariate Convex Orderings, Dependence, and Stochastic Equality

Part of: Distribution theory - Probability Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

Marco Scarsini
Marco Scarsini*
Affiliation:
Università D'Annunzio
*
∗Postal address: Dipartimento di Scienze, Università D'Annunzio, Viale Pindaro 42, I-65127 Pescara, Italy. e-mail address: [email protected]
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Abstract

We consider the convex ordering for random vectors and some weaker versions of it, like the convex ordering for linear combinations of random variables. First we establish conditions of stochastic equality for random vectors that are ordered by one of the convex orderings. Then we establish necessary and sufficient conditions for the convex ordering to hold in the case of multivariate normal distributions and sufficient conditions for the positive linear convex ordering (without the restriction to multi-normality).

Keywords

Dilationcopulalinear convex orderingstochastic dominancemultivariate normal distribution

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 60E15: Inequalities; stochastic orderings 62H99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 93 - 103
Copyright
Copyright © Applied Probability Trust 1998 

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