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Approximation of inverse moments of discrete distributions

Author

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  • Phillips, T.R.L.
  • Zhigljavsky, A.

Abstract

For a wide class of discrete distributions, we derive a representation of the inverse (negative) moments through the Stirling numbers of the first kind and inverse factorial moments. We specialize the results for the Poisson, binomial, hypergeometric and negative binomial distributions.

Suggested Citation

  • Phillips, T.R.L. & Zhigljavsky, A., 2014. "Approximation of inverse moments of discrete distributions," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 135-143.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:135-143
    DOI: 10.1016/j.spl.2014.07.007
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    References listed on IDEAS

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    1. Ramsay, Colin M., 1993. "A Note on Random Survivorship Group Benefits," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 149-156, May.
    2. Wuyungaowa & Wang, Tianming, 2008. "Asymptotic expansions for inverse moments of binomial and negative binomial," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3018-3022, December.
    3. Jones, C. Matthew & Zhigljavsky, Anatoly A., 2004. "Approximating the negative moments of the Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 171-181, January.
    4. Shi, Xiaoping & Wu, Yuehua & Liu, Yu, 2010. "A note on asymptotic approximations of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1260-1264, August.
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