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On the Use of Equispaced Discrete Distributions

Author

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  • Walhin, J.F.
  • Paris, J.

Abstract

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.

Suggested Citation

  • Walhin, J.F. & Paris, J., 1998. "On the Use of Equispaced Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 241-255, November.
    • Handle: RePEc:cup:astinb:v:28:y:1998:i:02:p:241-255_01
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    Cited by:

    1. Sangüesa, C., 2008. "Error bounds in approximations of random sums using gamma-type operators," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 484-491, April.
    2. Rafał Wójcik & Charlie Wusuo Liu & Jayanta Guin, 2019. "Direct and Hierarchical Models for Aggregating Spatially Dependent Catastrophe Risks," Risks, MDPI, vol. 7(2), pages 1-22, May.

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