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Statistical inference based on large claims via poisson approximation. Part II: Poisson process approach

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Blätter der DGVFM

Zusammenfassung

Es wird vorausgesetzt, daß für große Schadenhöhen die Annahme einer Pareto-Verteilung mit unbekanntem Gestaltparameter α und Skalenparameter g nahezu gerechtfertigt ist. Die Schätzung der unbekannten Parameter basiert auf den Exzedenten einer vorgegebenen Priorität. Der Schätzer wird von einem Maximum-Likelihood-Schätzer in einem parametrischen Modell von Poisson-Prozessen abgeleitet. Zu diesem Zweck wird eine Abschätzung für den Variationsabstand zwischen einem empirischen Punktprozeß und einem geeigneten Poisson-Prozeß angegeben. Weiterhin wird die asymptotische Normalität des Schätzers bewiesen.

Summary

In the present article we assume that the tail of the claim size distribution is of Pareto type. The estimator of the unknown parameters is based on the exceedances of a non-random threshold. The estimator is related to the maximum likelihood estimator in a parametric model of Poisson processes. For this purpose, we compare the model of empirical point processes and the model of Poisson processes. Moreover, we prove the asymptotic normality of the estimator.

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Authors and Affiliations

  1. Siegen

    Rolf-Dieter Reiss

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  1. Rolf-Dieter Reiss
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Reiss, RD. Statistical inference based on large claims via poisson approximation. Part II: Poisson process approach. Blätter DGVFM 19, 123–128 (1989). https://doi.org/10.1007/BF02809922

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  • DOI: https://doi.org/10.1007/BF02809922

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