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Approximation of sums by compound Poisson distributions with respect to stop-loss distances

Published online by Cambridge University Press:  01 July 2016

S. T. Rachev  and
L. Rüschendorf
S. T. Rachev*
Affiliation:
University of California, Santa Barbara
L. Rüschendorf*
Affiliation:
University of Munster
*
∗Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA. Supported by Deutsche Forschungsgemeinschaft Grant.
∗∗Postal address: Institut für Mathematische Statistik, Westfälische Wilhelms-Universität, Einsteinstrasse 62, 4400 Münster, W. Germany.
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Abstract

The approximation of sums of independent random variables by compound Poisson distributions with respect to stop-loss distances is investigated. These distances are motivated by risk-theoretic considerations. In contrast to the usual construction of approximating compound Poisson distributions, the method suggested in this paper is to fit several moments. For two moments, this can be achieved by scale transformations. It is shown that the new approximations are more stable and improve the usual approximations by accompanying laws in examples where the probability 1 – pi that the ith summand is zero is not too large.

Keywords

RISK THEORYINSURANCE MATHEMATICS
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 350 - 374
Copyright
Copyright © Applied Probability Trust 1990 

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