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Asymptotic results for FGM random sequences

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  • Hashorva, Enkelejd

Abstract

Let {Xn, n[greater-or-equal, slanted]1} be a centered FGM random sequence and put . Motivated by the dependence structure of FGM distributions (see, e.g. Johnson and Kotz, Comm. Statist. 4 (1977) 415) we derive almost sure and max-limit almost sure convergence for and Mn, respectively.

Suggested Citation

  • Hashorva, Enkelejd, 2001. "Asymptotic results for FGM random sequences," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 417-425, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:417-425
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    References listed on IDEAS

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    1. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    2. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    3. Hashorva, E. & Hüsler, J., 1999. "Extreme Values in FGM Random Sequences," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 212-225, February.
    4. Cambanis, Stamatis, 1977. "Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 551-559, December.
    5. Mikami, Toshio, 1997. "Large deviations and central limit theorems for Eyraud-Farlie-Gumbel-Morgenstern processes," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 73-78, August.
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    Cited by:

    1. Okolewski, A. & Kaluszka, M., 2015. "Stability of expected L-statistics against weak dependence of observations," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 157-164.

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