TY  - JOUR
A1  - Falk, Michael
A1  - Fuller, Timo
T1  - New characterizations of multivariate Max-domain of attraction and D-Norms
JF  - Extremes
N2  - In this paper we derive new results on multivariate extremes and D-norms. In particular we establish new characterizations of the multivariate max-domain of attraction property. The limit distribution of certain multivariate exceedances above high thresholds is derived, and the distribution of that generator of a D-norm on R\(^{d}\), whose components sum up to d, is obtained. Finally we introduce exchangeable D-norms and show that the set of exchangeable D-norms is a simplex.
KW  - extremal exchangeable D-norms
KW  - multivariate extreme value theory
KW  - multivariate max-domain of attraction
KW  - D-norm
KW  - generator of D-norm
KW  - multivariate exceedance
KW  - co-extremality coefficient
KW  - exchangeable D-norms
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-269071
SN  - 1572-915X
VL  - 24
IS  - 4
ER  - 
TY  - JOUR
A1  - Falk, Michael
A1  - Marohn, Frank
T1  - Von Mises condition revisited
N2  - It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.
KW  - Von Mises conditions
KW  - extreme value theory
KW  - extreme value distribution
KW  - extreme order statistics
KW  - generalized Pareto distribution
Y1  - 1993
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45790
ER  - 
TY  - JOUR
A1  - Falk, Michael
A1  - Marohn, Frank
T1  - Asymptotically optimal tests for conditional distributions
N2  - No abstract available
Y1  - 1993
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-45823
ER  -