caa a22 4500 605463697 CHVBK 20210128100254.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10687-014-0203-z doi (NATIONALLICENCE)springer-10.1007/s10687-014-0203-z Relations between the spectral measures and dependence of MEV distributions [Elektronische Daten] [Tiantian Mao, Taizhong Hu] The dependence structure of a multivariate extreme value (MEV) distribution is characterized by its spectral measure. In this paper, we investigate the interconnections between the supermodular ordering of two d-dimensional MEV distributions and the convex ordering of their spectral measures. The main result reveals some insightful understanding of the dependence structures of MEV distributions. More precisely, let G and G ∗ be two MEV distributions on R d with the corresponding univariate margins equal, and let S and S ∗ be their respective spectral measures with respect to the ℓ 1-norm ∥⋅∥. Suppose that W and W ∗ are two random vectors taking values on Θ = { 𝜃 ∈ R + d : ∥ 𝜃 ∥ = 1 } ${\Theta }=\{\theta \in \Re _{+}^{d}: \|\theta \|=1\}$ according to the probability laws S/d and S ∗/d, respectively. If W is smaller than W ∗ in the convex order, then G ∗ is smaller than G in the supermodular order. Several applications of the main result are also presented. Springer Science+Business Media New York, 2014 Multivariate extreme value distribution nationallicence Multivariate extreme value copula nationallicence Spectral measure nationallicence Simplex nationallicence Convex order nationallicence supermodular order nationallicence Convex transfer nationallicence Mao Tiantian Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, People's Republic of China aut Hu Taizhong Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, People's Republic of China aut Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 65-84 1386-1999 18:1<65 2015 18 10687 https://doi.org/10.1007/s10687-014-0203-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-014-0203-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mao Tiantian Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, People's Republic of China aut NATIONALLICENCE 700 1- Hu Taizhong Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, People's Republic of China aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/1(2015-03-01), 65-84 1386-1999 18:1<65 2015 18 10687