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A Note on Asymptotic Distribution of Products of Weighted Sums
Miao Yuyumiao728@yahoo.com.cnCollege of Mathematics and Information ScienceHenan Normal UniversityHenan, 453007, ChinaView full profile →
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- Received:
- 10 Jun 2011
- Accepted:
- 14 May 2012
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2012.10698611
- Pages:
- 99–105
Abstract
In this paper we establish the asymptotic distribution of products of weighted sums of independent, identically distributed, square integrable, positive random variable, which extends the results in Rempala and Wesołowski (2002).
Keywords
References
- Arnold Barry, C. and Villaseñr José, A.1999 . The asymptotic distribution of sums of records . , 1 ( 3 ) : 351 – 363 .
- István, Berkes and Herold, Dehling. 1993 . Some limit theorems in log density . , 21 : 1640 – 1670 .
- Khurelbaatar, Gonchigdanzan and Rempała, Grzegorz A.2006 . A note on the almost sure limit theorem for the product of partial sums . , 19 : 191 – 196 .
- William, Feller. 1971 . , Second , Vol. 2 , John Wiley and Sons, Inc .
- Wei, Huang and Lixin, Zhang. 2007 . A note on the invariance principle of the product of sums of random variables . , 12 : 51 – 56 .
- Xuewen, Lu and Yongcheng, Qi. 2004 . A note on asymptotic distribution of products of sums . , 68 ( 4 ) : 407 – 413 .
- Yu, Miao. 2008 . Central limit theorem and almost sure central limit theorem for the product of some partial sums . , 118 : 289 – 294 .
- Yu, Miao. 2009 . An extension of almost sure central limit theory for the product of partial sums . , 7 : 49 – 60 .
- Yu, Miao and Junfen, Li. 2010 . Asymptotic distribution of products of weighted sums of dependent random variables . , 7 ( 2 ) Article 11
- Yu, Miao and Jianyong, Mu. 2011 . Moderate deviations principle for products of sums of random variables . , 54 ( 4 ) : 769 – 784 .
- Yu, Miao and Bin, Qian. 2010 . A note on the exponential convergence rate for products of sums . , 62 ( 4 ) : 251 – 258 .
- Yongcheng, Qi. 2003 . Limit distributions for products of sums . , 62 ( 1 ) : 93 – 100 .
- Rempała, Grzegorz A. and Jacek, Wesołowski. 2002 . Asymptotics for products of sums and -statistics . , 7 : 47 – 54 .
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