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A note on asymptotic distribution of products of sums

Author

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  • Lu, Xuewen
  • Qi, Yongcheng

Abstract

The asymptotic behavior of product of the partial sums from a sequence of independent and identically distributed positive random variables have been studied by several papers. In Qi (Statist. Probab. Lett. 62 (2003) 93) the limit distribution for properly normalized products is proved when the underling distribution is in the domain of attraction of a stable law with exponent in (1,2]. In this note a similar result is obtained when the underlying distribution is in the domain of attraction of a stable law with exponent 1 and has a finite first moment.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:4:p:407-413
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    References listed on IDEAS

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    1. Qi, Yongcheng, 2003. "Limit distributions for products of sums," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 93-100, March.
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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. Kosinski, Kamil, 2009. "Asymptotics for sums of a function of normalized independent sums," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 415-419, February.
    3. 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.
    4. 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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    1. 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.
    2. 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.
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    6. 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.
    7. Kosinski, Kamil, 2009. "Asymptotics for sums of a function of normalized independent sums," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 415-419, February.

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