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Improved bounds for approximations to compound distributions

Author

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  • Upadhye, N.S.
  • Vellaisamy, P.

Abstract

In this work, we consider compound negative binomial and compound Poisson approximations to the generalized Poisson–binomial distribution. We derive some total variation upper bounds which improve on the existing results in terms of the order of approximation. An application is also discussed.

Suggested Citation

  • Upadhye, N.S. & Vellaisamy, P., 2013. "Improved bounds for approximations to compound distributions," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 467-473.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:467-473
    DOI: 10.1016/j.spl.2012.10.021
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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(1), pages 187-210, March.
    2. 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.
    3. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    4. Steve Drekic & Gordon Willmot, 2005. "On the Moments of the Time of Ruin with Applications to Phase-Type Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 17-30.
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