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A Note on the Inverse Moment for the Non Negative Random Variables

Author

Listed:
  • Shuhe Hu
  • Xinghui Wang
  • Wenzhi Yang
  • Xuejun Wang

Abstract

Let {Zn} be a sequence of non negative random variables satisfying a Rosenthal-type inequality and Xn=Mn-1∑i=1nZi$X_n=M_n^{-1}\sum \nolimits _{i=1}^n Z_i$, where {Mn} is a sequence of positive real numbers. By using the Rosenthal-type inequality, the inverse moment E(a + Xn)− α can be asymptotically approximated by (a + EXn)− α for all a > 0 and α > 0. Furthermore, we show that E[f(Xn)]− 1 can be asymptotically approximated by [f(EXn)]− 1 for a function f( · ) satisfying certain conditions. Our results generalize and improve some corresponding results, which can allow immediate applications to compute the inverse moments for the non negative random variables whose distributions are such as Binomial distribution, Poisson distribution, Gamma distribution, etc.

Suggested Citation

  • Shuhe Hu & Xinghui Wang & Wenzhi Yang & Xuejun Wang, 2014. "A Note on the Inverse Moment for the Non Negative Random Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1750-1757, April.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:8:p:1750-1757
    DOI: 10.1080/03610926.2012.673677
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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. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.

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