Stability of Random Sums

Details Stability of Random Sums Stability of Random Sums

2003-11-20

arxiv.org/abs/math/0311348v1

Stochastic Modelling and Applications, Year 2002, Vol.5, No.1, p.17-26

Mathematics

Probability

10 pages, in PDF format, a reference added in the abstract here

Scientific paper

When the distribution of a random (N) sum of independent copies of a r.v X is of the same type as that of X we say that X is N-sum stable. In this paper we consider a generalization of stability of geometric sums by studying distributions that are stable under summation w.r.t Harris law. We show that the notion of stability of random sums can be extended to include the case when X is discrete. Finally we propose a method to identify the probability law of N for which X is N-sum stable. See also Satheesh and Nair (2002), (Some classes of distributions on ther non-negative lattice, J. Ind. Statist. Assoc., 2002, 40, 41-58) for a study of discrete laws of the same type and stability of geometric sums of discrete laws.

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