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A note on asymptotic approximations of inverse moments of nonnegative random variables

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  • Shi, Xiaoping
  • Wu, Yuehua
  • Liu, Yu

Abstract

Let {Zn} be a sequence of independently distributed and nonnegative random variables and let . We show that, under mild conditions, E[(a+Xn)-[alpha]] can be asymptotically approximated by [a+E(Xn)]-[alpha] for a>0 and [alpha]>0. We further show that E{[f(Xn)]-1} can be asymptotically approximated by {f[E(Xn)]}-1 for a function f([dot operator]) satisfying certain conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1260-1264
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    References listed on IDEAS

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    1. Garcia, Nancy Lopes & Palacios, José Luis, 2001. "On inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 235-239, June.
    2. Kaluszka, M. & Okolewski, A., 2004. "On Fatou-type lemma for monotone moments of weakly convergent random variables," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 45-50, January.
    3. Ramsay, Colin M., 1993. "A Note on Random Survivorship Group Benefits," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 149-156, May.
    4. Pittenger, A. O., 1990. "Sharp mean-variance bounds for Jensen-type inequalities," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 91-94, July.
    5. Wu, Tiee-Jian & Shi, Xiaoping & Miao, Baiqi, 2009. "Asymptotic approximation of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1366-1371, June.
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    Cited by:

    1. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    2. Phillips, T.R.L. & Zhigljavsky, A., 2014. "Approximation of inverse moments of discrete distributions," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 135-143.
    3. Anne Philippe & Caroline Robet & Marie-Claude Viano, 2021. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 375-400, April.

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