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An almost sure central limit theorem for products of sums under association

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  • Li, Yun-Xia
  • Wang, Jian-Feng

Abstract

Let {Xn,n[greater-or-equal, slanted]1} be a strictly stationary positively or negatively associated sequence of positive random variables with and . Denote and [gamma]=[sigma]/[mu] the coefficient of variation. Under suitable conditions, we show thatwhere , F(·) is the distribution function of the random variable , and is a standard normal random variable. This extends the earlier work on independent, positive random variables (see Khurelbaatar and Rempala [2006. A note on the almost sure limit theorem for the product of partial sums. Appl. Math. Lett. 19, 191-196]).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:4:p:367-375
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    References listed on IDEAS

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    1. Peligrad, Magda & Shao, Qi-Man, 1995. "A note on the almost sure central limit theorem for weakly dependent random variables," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 131-136, February.
    2. Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    3. 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.
    4. Qi, Yongcheng, 2003. "Limit distributions for products of sums," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 93-100, March.
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