Zusammenfassung
Wir stellen eine neue SchÄtzmethode für den rechten Tail einer subexponentiellen Verteilung vor. Ausgehend von einem semiparametrischen Modell schÄtzen wir Parameter mittels der oberen Ord nungsstatistiken einer Stichprobe. Wir beweisen Konsistenz und asymptotische NormalitÄt der SchÄtzer. Ihre Eigenschaften für kleine Stichprohen untersuchen wir mittels Monte-Carlo-Simula tion. Schlie\lich wenden wir die SchÄtzmethode auf eine Stichprobe von Autohaftpflichtdaten aus einem Schadenexzedentenvertrag an.
Summary
We propose a new estimation procedure for the right tail of a subexponential distribution, which is based on the upper order statistics of a sample. We prove weak convergence and asymptotic normality of our estimators. Furthermore, we review their small sample properties which have been studied by Monte Carlo simulation. Finally, we apply the estimation procedure to a sample of automobile liability data from an excess of loss reinsurance treaty.
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Klüppelberg, C., Villaseñor, J.A. Estimation of distribution tails —a semiparametric approach. Blätter DGVFM 21, 213–235 (1993). https://doi.org/10.1007/BF02809405
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DOI: https://doi.org/10.1007/BF02809405