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Recursions for Convolutions of Arithmetic Distributions

  • Nelson De Pril (a1)

Abstract

A simple recursion for the n-fold convolution of an arithmetic distribution with itself is developed and its relation to Panjer's algorithm for compound distributions is shown.

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Copyright

References

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Adelson, R. M. (1966) Compound Poisson distributions. Operations Research Quarterly 17, 7375.
Bühlmann, H. and Gerber, H. U. (1980) Discussion of “The aggregate claims distribution and stop-loss reinsurance” by H. H. Panjer. Transactions of the Society of Actuaries 32, 537538.
Henrici, P. (1956) Automatic computations with power series, Journal of the Association for Computing Machinery 3, 1015.
Jewell, W. S. and Sundt, B. (1981) Improved approximations forthe distribution of a heterogeneous risk portfolio. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 1981, 221240.
Katti, S. K. and Gurland, J. (1958) Some families of contagious distributions. Air Force Technical Note, Air Force Office of Scientific Research Contract AF 49(638)-43, Technical Note No. TN 59-4 AD 208184.
Knuth, D. E. (1969) The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Addison-Wesley Series in Computer Science and Information Processing.
Panjer, H. H. (1981) Recursive evaluation of a family of compound distributions. Astin Bulletin 12, 2226.
Shumway, R. and Gurland, J. (1960) A fitting procedure for some generalized Poisson distributions. Skandinavisk Aktuarietidskrift 43, 87108.

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