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Limit distributions for products of sums

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  • Qi, Yongcheng

Abstract

Let {X,Xn, n[greater-or-equal, slanted]1} be a sequence of independent and identically distributed positive random variables and set Sn=[summation operator]j=1n Xj for n[greater-or-equal, slanted]1. This paper proves that properly normalized products of the partial sums, ([product operator]j=1nSj/n![mu]n)[mu]/An, converges in distribution to some nondegenerate distribution when X is in the domain of attraction of a stable law with index [alpha][set membership, variant](1,2].

Suggested Citation

  • Qi, Yongcheng, 2003. "Limit distributions for products of sums," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 93-100, March.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:1:p:93-100
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    Citations

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    Cited by:

    1. Kosinski, Kamil M., 2009. "On the functional limits for sums of a function of partial sums," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1522-1527, July.
    2. Lu, Xuewen & Qi, Yongcheng, 2004. "A note on asymptotic distribution of products of sums," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 407-413, July.
    3. Kosinski, Kamil, 2009. "Asymptotics for sums of a function of normalized independent sums," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 415-419, February.
    4. Rempala, Grzegorz & Wesolowski, Jacek, 2005. "Asymptotics for products of independent sums with an application to Wishart determinants," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 129-138, September.
    5. Gonchigdanzan, Khurelbaatar & Kosinski, Kamil M., 2009. "On the functional limits for partial sums under stable law," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1818-1822, September.
    6. Yun-Xia Li & Jian-Feng Wang, 2007. "Asymptotic distribution for products of sums under dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(1), pages 75-87, July.
    7. Gonchigdanzan, Khurelbaatar, 2008. "An almost sure limit theorem for the product of partial sums with stable distribution," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3170-3175, December.
    8. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.

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