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Asymptotic approximation of inverse moments of nonnegative random variables

Author

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  • Wu, Tiee-Jian
  • Shi, Xiaoping
  • Miao, Baiqi

Abstract

Let be a sequence of independent nonnegative r.v.'s (random variables) with finite second moments. It is shown that under a Lindeberg-type condition, the [alpha]th inverse moment E{a+Xn}-[alpha] can be asymptotically approximated by the inverse of the [alpha]th moment {a+EXn}-[alpha] where , and {Xn} are the naturally-scaled partial sums. Furthermore, it is shown that, when {Zn} only possess finite rth moments, 1

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:11:p:1366-1371
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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.
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    Cited by:

    1. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    2. 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.
    3. 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.
    4. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.

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