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Approximation of Sums by Compound Poisson Distributions with Respect to Stop-Loss Distances

S. T. Rachev and L. Rüschendorf
Advances in Applied Probability
Vol. 22, No. 2 (Jun., 1990), pp. 350-374
DOI: 10.2307/1427540
Stable URL: http://www.jstor.org/stable/1427540
Page Count: 25
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Approximation of Sums by Compound Poisson Distributions with Respect to Stop-Loss Distances
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Abstract

The approximation of sums of independent random variables by compound Poisson distributions with respect to stop-loss distances is investigated. These distances are motivated by risk-theoretic considerations. In contrast to the usual construction of approximating compound Poisson distributions, the method suggested in this paper is to fit several moments. For two moments, this can be achieved by scale transformations. It is shown that the new approximations are more stable and improve the usual approximations by accompanying laws in examples where the probability 1-pi that the ith summand is zero is not too large.

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