Author:
Roos Bero,Pfeifer Dietmar
Abstract
In this paper, we consider the total variation distance between the distributions of two random sums SM and SN with different random summation indices M and N. We derive upper bounds, some of which are sharp. Further, bounds with so-called magic factors are possible. Better results are possible when M and N are stochastically or stop-loss ordered. It turns out that the solution of this approximation problem strongly depends on how many of the first moments of M and N coincide. As approximations, we therefore choose suitable finite signed measures, which coincide with the distribution of the approximating random sum SN if M and N have the same first moments.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
2 articles.
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