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Some Moment Relations for the Hipp approximation

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  • Dhaene, Jan
  • Sundt, Bjørn
  • De Pril, Nelson

Abstract

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.

Suggested Citation

  • Dhaene, Jan & Sundt, Bjørn & De Pril, Nelson, 1996. "Some Moment Relations for the Hipp approximation," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 117-121, May.
    • Handle: RePEc:cup:astinb:v:26:y:1996:i:01:p:117-121_00
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    Cited by:

    1. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    2. Sundt, Bjorn, 2000. "On error bounds for approximations to multivariate distributions," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 137-144, August.

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