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Stability of sums of weighted nonnegative random variables

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  • Etemadi, N.

Abstract

A stability result for sums of weighted nonnegative random variables is established and then it is utilized to obtain, among other things, a slight generalization of the Borel-Cantelli lemma and to show that the work of Jamison, Orey, and Pruitt (Z. Wahrsch. Verw. Gebiete 4 (1965), 40-44) on almost sure convergence of weighted averages of independent random variables remains valid if the assumption of independence on the random variables is replaced by pairwise independence.

Suggested Citation

  • Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:2:p:361-365
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    Cited by:

    1. Etemadi, N., 2007. "Stability of weighted averages of 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 389-395, February.
    2. Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    3. Berti, Patrizia & Rigo, Pietro, 2002. "A uniform limit theorem for predictive distributions," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 113-120, January.
    4. Chen, Pingyan & Sung, Soo Hak, 2016. "A strong law of large numbers for nonnegative random variables and applications," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 80-86.
    5. H. Jabbari, 2013. "On almost sure convergence for weighted sums of pairwise negatively quadrant dependent random variables," Statistical Papers, Springer, vol. 54(3), pages 765-772, August.
    6. Matula, Przemyslaw, 2005. "On almost sure limit theorems for positively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 59-66, August.
    7. Hashorva, Enkelejd, 2001. "Asymptotic results for FGM random sequences," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 417-425, October.

    More about this item

    Keywords

    Sure convergence stability of sums;

    Statistics

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