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Estimation of a bivariate extreme value distribution. (English) Zbl 1008.62053
For a bivariate r.v. \((Z_1,Z_2)\) with unit Fréchet margins a dependence function \(A^*\) (if it exists) is defined by \[ \Pr\{Z_1<z_1,Z_2<z_2)=\exp\left(-(z_1^{-1}+z_2^{-1})A^*(z_2(z_1+z_2)^{-1}\right). \] It also can be defined in terms of a spectral measure. The authors introduce a new nonparametric estimator for \(A^*\) by i.i.d. samples, demonstrate its consistency and compare it with some other estimators via simulation studies.

MSC:
62G32 Statistics of extreme values; tail inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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