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Compound Poisson approximation to weighted sums of symmetric discrete variables

Author

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  • A. Elijio
  • V. Čekanavičius

Abstract

The weighted sum $$S=w_1S_1+w_2S_2+\cdots +w_NS_N$$ S = w 1 S 1 + w 2 S 2 + ⋯ + w N S N is approximated by compound Poisson distribution. Here $$S_i$$ S i are sums of symmetric independent identically distributed discrete random variables, and $$w_i$$ w i denote weights. The estimates take into account the smoothing effect that sums $$S_i$$ S i have on each other. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • A. Elijio & V. Čekanavičius, 2015. "Compound Poisson approximation to weighted sums of symmetric discrete variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 195-210, February.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:1:p:195-210
    DOI: 10.1007/s10463-013-0445-6
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    References listed on IDEAS

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    1. Vydas Čekanavičius & Bero Roos, 2006. "Compound binomial approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 815-815, December.
    2. Booth, J. G. & Hall, P. & Wood, A. T. A., 1994. "On the Validity of Edgeworth and Saddlepoint Approximations," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 121-138, October.
    3. Rosalsky, Andrew & Sreehari, M., 1998. "On the limiting behavior of randomly weighted partial sums," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 403-410, November.
    4. Vydas Čekanavičius & Bero Roos, 2006. "Compound Binomial Approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 187-210, March.
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