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On the Use of Equispaced Discrete Distributions

Published online by Cambridge University Press:  29 August 2014

J.F. Walhin  and
J. Paris
J.F. Walhin*
Affiliation:
Institut de Statistique, Université Catholique de Louvain, Belgium Le Mans Assurances, Belgique
J. Paris*
Affiliation:
Institut de Statistique, Université Catholique de Louvain, Belgium
*
*Institut de Statistique, Voie du Roman Pays, 20 B-1348 Louvain-la-Neuve, Belgique
•Le Mans Assurances, Avenue Louise, 222 B-1050 Bruxelles, Belgique
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Abstract

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The Kolmogorov distance is used to transform arithmetic severities into equispaced arithmetic severities in order to reduce the number of calculations when using algorithms like Panjer's formulae for compound distributions. An upper bound is given for the Kolmogorov distance between the true compound distribution and the transformed one. Advantages of the Kolmogorov distance and disadvantages of the total variation distance are discussed. When the bounds are too big, a Berry-Esseen result can be used. Then almost every case can be handled by the techniques described in this paper. Numerical examples show the interest of the methods.

Keywords

Recursive formulacompound distributioninfinite divisibilityequispaced discrete distributionKolmogorov distancetotal variation distanceupper and lower boundsBerry-Esseen bound
Type
Workshops
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 2 , November 1998 , pp. 241 - 255
Copyright
Copyright © International Actuarial Association 1998

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