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Compound Poisson approximation to weighted sums of symmetric discrete variables

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Abstract

The weighted sum \(S=w_1S_1+w_2S_2+\cdots +w_NS_N\) is approximated by compound Poisson distribution. Here \(S_i\) are sums of symmetric independent identically distributed discrete random variables, and \(w_i\) denote weights. The estimates take into account the smoothing effect that sums \(S_i\) have on each other.

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Acknowledgments

The authors wish to thank the referee for constructive suggestions which improved the paper.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius , 03225, Lithuania

    A. Elijio & V. Čekanavičius

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  1. A. Elijio
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  2. V. Čekanavičius
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Correspondence to V. Čekanavičius.

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Elijio, A., Čekanavičius, V. Compound Poisson approximation to weighted sums of symmetric discrete variables. Ann Inst Stat Math 67, 195–210 (2015). https://doi.org/10.1007/s10463-013-0445-6

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  • DOI: https://doi.org/10.1007/s10463-013-0445-6

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