Journal of Mathematical Sciences

, Volume 92, Issue 4, pp 4038–4043 | Cite as

On moments of counting distributions satisfying thekth-order recursion and their compound distributions

  • M. Murat
  • D. Szynal


We present formulas and recurrence formulas commonly used in insurance mathematics for moments of counting distributions given by the kth-order recursion. Moreover, we develop recurrence formulas for moments of compound distributions with those counting distributions satisfying the kth-order recursion.


Probability Function Recurrence Relation Negative Binomial Distribution Central Moment Recurrence Formula 
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  1. 1.
    P. Delaporte, “Quelques problémes de statistique mathématique posés par l'assurance automobile et le bonus pour non sinistre,”Bulletin Trimestriel de l'Institut des Actuaries Française,227, 87–102 (1959).Google Scholar
  2. 2.
    P. Delaporte, “Un probléme de l'assurance accidents d'automobiles examiné par la statistique mathématique,” in:Transactions of the XVIth International Congress of Actuaries II (1960), pp. 121–135.Google Scholar
  3. 3.
    N. De Pril, “Moments of a class of compound distributions,”Scand. Actuarial J., 22–26 (1981).Google Scholar
  4. 4.
    K. J. Schröter, “On a family of counting distributions and recursions for related compound distributions.”Scand. Actuarial J., 161–175 (1990).Google Scholar
  5. 5.
    B. Sundt and W. S. Jewell, “Further results on recursive evaluation of compound distributions,”ASTIN Bulletin,12, 27–39 (1981).MathSciNetGoogle Scholar
  6. 6.
    B. Sundt, “On some extensions of Panjer's class of counting distributions,”ASTIN Bulletin,22, 61–80 (1992).CrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • M. Murat
    • 1
  • D. Szynal
    • 1
  1. 1.Department of MathematicsTechnical University of LublinLublinPoland

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