## Von Mises condition revisited

Please always quote using this URN: urn:nbn:de:bvb:20-opus-45790

- 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 truncatedIt 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.…

Author: | Michael Falk, Frank Marohn |
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URN: | urn:nbn:de:bvb:20-opus-45790 |

Document Type: | Journal article |

Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |

Language: | English |

Year of Completion: | 1993 |

Source: | In: The Annals of Probability (1993) 21, 3, 1310 - 1328 |

Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Tag: | Von Mises conditions; extreme order statistics; extreme value distribution; extreme value theory; generalized Pareto distribution |

Release Date: | 2010/04/26 |