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Further improved recursions for a class of compound Poisson distributions

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  • Chadjiconstantinidis, Stathis
  • Pitselis, Georgios

Abstract

In the present paper we develop more efficient recursive formulae for the evaluation of the t-order cumulative function [Gamma]th(x) and the t-order tail probability [Lambda]th(x) of the class of compound Poisson distributions in the case where the derivative of the probability generating function of the claim amounts can be written as a ratio of two polynomials. These efficient recursions can be applied for the exact evaluation of the probability function (given by De Pril [De Pril, N., 1986a. Improved recursions for some compound Poisson distributions. Insurance Math. Econom. 5, 129-132]), distribution function, tail probability, stop-loss premiums and t-order moments of stop-loss transforms of compound Poisson distributions. Also, efficient recursive algorithms are given for the evaluation of higher-order moments and r-order factorial moments about any point for this class of compound Poisson distributions. Finally, several examples of discrete claim size distributions belonging to this class are also given.

Suggested Citation

  • Chadjiconstantinidis, Stathis & Pitselis, Georgios, 2009. "Further improved recursions for a class of compound Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 278-286, April.
    • Handle: RePEc:eee:insuma:v:44:y:2009:i:2:p:278-286
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    References listed on IDEAS

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    1. Sundt, Bjorn, 2002. "Recursive evaluation of aggregate claims distributions," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 297-322, June.
    2. De Pril, Nelson, 1986. "Improved recursions for some compound poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 129-132, April.
    3. Waldmann, Karl-Heinz, 1996. "Modified Recursions for a Class of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 213-224, November.
    4. Sundt, Bjorn, 2003. "Some recursions for moments of compound distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 487-496, December.
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