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Recursions for Convolutions of Arithmetic Distributions

Published online by Cambridge University Press:  29 August 2014

Nelson De Pril*
Affiliation:
Instituut voor Actuariële Wetenschappen, K. U. Leuven, Belgium
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Abstract

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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.

Type
Articles
Copyright
Copyright © International Actuarial Association 1985

References

Adelson, R. M. (1966) Compound Poisson distributions. Operations Research Quarterly 17, 7375.CrossRefGoogle Scholar
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.Google Scholar
Henrici, P. (1956) Automatic computations with power series, Journal of the Association for Computing Machinery 3, 1015.CrossRefGoogle Scholar
Jewell, W. S. and Sundt, B. (1981) Improved approximations forthe distribution of a heterogeneous risk portfolio. Mitteilungen der Vereinigung schweizerischer Versicherungsmathematiker 1981, 221240.Google Scholar
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.Google Scholar
Knuth, D. E. (1969) The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Addison-Wesley Series in Computer Science and Information Processing.Google Scholar
Panjer, H. H. (1981) Recursive evaluation of a family of compound distributions. Astin Bulletin 12, 2226.CrossRefGoogle Scholar
Shumway, R. and Gurland, J. (1960) A fitting procedure for some generalized Poisson distributions. Skandinavisk Aktuarietidskrift 43, 87108.Google Scholar