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On the Lagrangian Katz family of distributions as a claim frequency model

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  • Gathy, Maude
  • Lefèvre, Claude

Abstract

The Panjer (Katz) family of distributions is defined by a particular first-order recursion which is built on the basis of two parameters. It is known to characterize the Poisson, negative binomial and binomial distributions. In insurance, its main usefulness is to yield a simple recursive algorithm for the aggregate claims distribution. The present paper is concerned with the more general Lagrangian Katz family of distributions. That family satisfies an extended recursion which now depends on three parameters. To begin with, this recursion is derived through a certain first-crossing problem and two applications in risk theory are described. The distributions covered by the recursion are then identified as the generalized Poisson, generalized negative binomial and binomial distributions. A few other properties of the family are pointed out, including the index of dispersion, an extended Panjer algorithm for compound sums and the asymptotic tail behaviour. Finally, the relevance of the family is illustrated with several data sets on the frequency of car accidents.

Suggested Citation

  • Gathy, Maude & Lefèvre, Claude, 2010. "On the Lagrangian Katz family of distributions as a claim frequency model," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 76-83, August.
  • Handle: RePEc:eee:insuma:v:47:y:2010:i:1:p:76-83
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    References listed on IDEAS

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    1. Jewell, William S., 1984. "Approximating the Distribution of a Dynamic Risk Portfolio," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 14(02), pages 135-148, October.
    2. Goovaerts, M. J. & Kaas, R., 1991. "Evaluating Compound Generalized Poisson Distributions Recursively," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 21(02), pages 193-198, November.
    3. Ambagaspitiya, Rohana S., 1998. "Compound bivariate Lagrangian Poisson distributions," Insurance: Mathematics and Economics, Elsevier, vol. 23(1), pages 21-31, October.
    4. H. Panjer, Harry & Shaun Wang, 2, 1993. "On the Stability of Recursive Formulas," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(02), pages 227-258, November.
    5. Claude Lefèvre & Stéphane Loisel, 2008. "On Finite-Time Ruin Probabilities for Classical Risk Models," Post-Print hal-00168958, HAL.
    6. Vernic, Raluca, 2000. "A Multivariate Generalization of the Generalized Poisson Distribution," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(01), pages 57-67, May.
    7. Ambagaspitiya, R. S., 1995. "A family of discrete distributions," Insurance: Mathematics and Economics, Elsevier, vol. 16(2), pages 107-127, May.
    8. Ambagaspitiya, R.S. & Balakrishnan, N., 1994. "On the Compound Generalized Poisson Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 24(02), pages 255-263, November.
    9. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 29(02), pages 315-325, November.
    10. Embrechts, Paul & Maejima, Makoto & Teugels, Jozef L., 1985. "Asymptotic Behaviour of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 15(01), pages 45-48, April.
    11. Denuit, Michel, 1997. "A New Distribution of Poisson-Type for the Number of Claims," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(02), pages 229-242, November.
    12. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(01), pages 22-26, June.
    13. Sundt, Bjørn & Jewell, William S., 1981. "Further Results on Recursive Evaluation of Compound Distributions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 12(01), pages 27-39, June.
    14. Sundt, Bjørn, 2000. "On Multivariate Vernic Recursions," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 30(01), pages 111-122, May.
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    Cited by:

    1. Zhao, Xiaobing & Zhou, Xian, 2012. "Copula models for insurance claim numbers with excess zeros and time-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 191-199.

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