# Compound poisson approximation for the distribution of extremes

Article

Novak, S., Barbour, A. and Xia, A. 2002. Compound poisson approximation for the distribution of extremes.

*Advances in applied probability.*34 (1), pp. 223-240. https://doi.org/10.1239/aap/1019160958

Type | Article |
---|---|

Title | Compound poisson approximation for the distribution of extremes |

Authors | Novak, S., Barbour, A. and Xia, A. |

Abstract | Empirical point processes of exceedances play an important role in extreme value theory, and their limiting behaviour has been extensively studied. Here, we provide explicit bounds on the accuracy of approximating an exceedance process by a compound Poisson or Poisson cluster process, in terms of a Wasserstein metric that is generally more suitable for the purpose than the total variation metric. The bounds only involve properties of the finite, empirical sequence that is under consideration, and not of any limiting process. The argument uses Bernstein blocks and Lindeberg's method of compositions. |

Publisher | Applied Probability Trust |

Journal | Advances in applied probability |

ISSN | 0001-8678 |

Publication dates | |

Print | 2002 |

Publication process dates | |

Deposited | 25 Mar 2009 |

Output status | Published |

Digital Object Identifier (DOI) | https://doi.org/10.1239/aap/1019160958 |

Language | English |

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https://repository.mdx.ac.uk/item/8163x

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