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Some Moment Relations for the Hipp approximation

Published online by Cambridge University Press:  29 August 2014

Jan Dhaene ,
Bjørn Sundt  and
Nelson De Pril
Jan Dhaene*
Affiliation:
Katholieke Universiteit Leuven
Bjørn Sundt*
Affiliation:
University of Bergen
Nelson De Pril*
Affiliation:
Katholieke Universiteit Leuven
*
Departement Toegepaste Economische Wetenschappen, Katholieke Universiteit Leuven, Huis Eighen Heerd, Minderbroederstraat 5, B-3000 Leuven, Belgium
Department of Mathematics, University of Bergen, Allégaten 55, N-5007 Bergen, Norway
Departement Toegepaste Economische Wetenschappen, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000 Leuven, Belgium
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Abstract

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In the present note we consider the Hipp approximation to the convolution of a finite number of probability distributions on the non-negative integers. It is shown that the moment up to and including order r of the rth order approximation are equal to the corresponding moments of the exact distribution. We also give a relation between the exact and approximated (r + 1)th order moments and indicate how similar relations can be obtained for higher order moments.

Keywords

Hipp approximationmoments
Type
Short Contribution
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 117 - 121
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

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Dhaene, J. & De Pril, N. (1994). On a class of approximative computation methods in the individual model. Insurance: Mathematics and Economics, 14, 181–196.Google Scholar
Hipp, C. (1986). Improved approximations for the aggregate claims distribution in the individual model. ASTIN Bulletin 16, 89–100.CrossRefGoogle Scholar
Hipp, C. & Michel, R. (1990). Risikotheorie: Stochastische Modelle und Statistische Methoden. Verlag Versicherungswirtschaft e.V., Karlruhe.Google Scholar