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The Panjer recursion makes use of this iterative relationship to specify a recursive way of constructing the probability distribution of ''S''. In the following <math>W_N(x)\,</math> denotes the [[probability generating function]] of ''N'': for this see the table in [[(a,b,0) class of distributions]].
In the case of claim number is known, please note the ''De Pril'' algorithm<ref>Vose Software Risk Wiki: http://www.vosesoftware.com/riskwiki/Aggregatemodeling-DePrilsrecursivemethod.php</ref>. This algorithm is suitable to compute the sum distribution of <math>n</math> discrete [[random variables]].<ref>{{Cite journal | doi = 10.1080/03461238.1988.10413837| title = Improved approximations for the aggregate claims distribution of a life insurance portfolio| journal = Scandinavian Actuarial Journal| volume = 1988| pages = 61| year = 1988| last1 = De Pril | first1 = N. }}</ref>
== Recursion ==
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