TY - JOUR

T1 - Inequalities for the extremal coefficients of multivariate extreme value distributions.

AU - Schlather, Martin

AU - Tawn, Jonathan A.

PY - 2002/3

Y1 - 2002/3

N2 - The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.

AB - The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.

KW - dependence measures - extremal coefficient - multivariate extreme value distribution - inequalities - self-consistency

U2 - 10.1023/A:1020938210765

DO - 10.1023/A:1020938210765

M3 - Journal article

VL - 5

SP - 87

EP - 102

JO - Extremes

JF - Extremes

SN - 1386-1999

IS - 1

ER -