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The class of sum-geometric infinitely divisible distributions of order \(k\). (English) Zbl 0923.60019

Based on a generalization \(G(p,k)\) of the usual geometric distribution the distribution of a random vector \(Y\) is called sum-geometric infinitely divisible of order \(k\) if, for each \(0<p<1\), \(Y\) can be written in the form \(Y=\sum^N_{i=1} X_i\) with \(N,X_1,X_2, \dots\) independent, \(X_1,X_2, \dots\) identically distributed and \(N\) \(G(p,k)\)-distributed. Aspects of these distributions are investigated, mainly via their characteristic functions, and some examples and applications are given.

MSC:

60E07 Infinitely divisible distributions; stable distributions
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