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Some Remarks on the Supermodular Order

✍ Scribed by Alfred Müller; Marco Scarsini

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
170 KB
Volume
73
Category
Article
ISSN
0047-259X

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✦ Synopsis

In this paper we solve two open problems posed by Joe (1997) concerning the supermodular order. First we give an example which shows that the supermodular order is strictly stronger than the concordance order for dimension d=3. Second we show that the supermodular order fulfils all desirable properties of a multivariate positive dependence order. We especially prove the non-trivial fact that it is closed with respect to weak convergence. This is applied to give a complete characterization of the supermodular order for multivariate normal distributions.

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