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Sundt and Jewell's Family of Discrete Distributions

  • Gordon Willmot (a1)
Abstract

A class of claim frequency distributions discussed by Sundt and Jewell (1981) is completely enumerated. Computational techniques for the associated compound total claims distribution in the presence of policy modifications are then derived.

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Copyright
Corresponding author
University of Waterloo, Faculty of Mathematics, Department of Statistics and Actuarial Science, Waterloo, Ontario N2L 3G1, Canada.
References
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Embrechts, P., Maejima, M., and Teugels, J. (1985) Asymptotic behaviour of compound distributions. ASTIN Bulletin 15, 4548.
Engen, S. (1974) On species frequency models. Biomelrika 61, 263270.
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1 (3rd edn). Wiley, New York.
Gossiaux, A. and Lemaire, J. (1981) Methodes d'ajustement de distributions de Sinistres. Bulletin of the Association of Swiss Actuaries 81, 8795.
Jewell, W. and Sundt, B. (1981) Improved approximations for the distribution of a heterogeneous risk portfolio. Bulletin of the Association of Swiss Actuaries 81, 221240.
Karlin, S. and Taylor, H. (1981) A Second Course in Stochastic Processes. Academic Press, New York.
Marsden, J. (1974) Elementary Classical Analysis. W. H. Freeman, San Fransisco.
Panjer, H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 2226.
Panjer, H. and Willmot, G. (1984) Computational techniques in reinsurance models. Transactions of the 22nd International Congress of Actuaries, Sydney, 4, 111120.
Ströter, B. (1985) The numerical evaluation of the aggregate claim density function via integral equations. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 17, 114.
Sundt, B. and Jewell, W. (1981) Further results on recursive evaluation of compound distributions. ASTIN Bulletin 12, 2739.
Wani, J. and Lo, H. (1983) A characterization of invariant power series abundance distributions. Canadian Journal of Statistics 11, 317323.
Wani, J. and Lo, H. (1986) Selecting a power-series distribution for goodness of fit. Canadian Journal of Statistics 14, 347353.
Willmot, G. (1986) Mixed compound Poisson distributions. ASTIN Bulletin 16S, S59S79.
Willmot, G. and Panjer, H. (1987) Difference equation approaches in evaluation of compound distributions. Insurance: Mathematics and Economics 6, 4356.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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