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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (5): 538-541    DOI: 10.3785/j.issn.1008-9497.2017.05.007
数学与计算机科学     
行为两两NQD随机变量阵列加权和的完全收敛性
章茜
浙江机电职业技术学院 数学教研室, 浙江 杭州 310053
Complete convergence for weighted sums of arrays with row-wise pairwise negatively quadrant dependent sequences
ZHANG Qian
Mathematics Teaching and Research Section, Zhejiang Institute of Mechanical and Electrical Engineering, Hangzhou 310053, China
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摘要： 负相依在统计分析和可靠性理论中有着广泛的应用.研究了一类行为两两NQD随机变量阵列加权和的完全收敛性.利用矩不等式和有效的截尾方法，建立了行为两两NQD随机变量阵列加权和的完全收敛性的充要条件，从而推广了吴群英等建立的关于一类NA随机变量序列的完全收敛性的结论.
关键词： 行为两两NQD阵列;  加权和;  完全收敛性    
Abstract: Negative dependence is important and widely used in multivariate statistical analysis and reliability theory. The purpose of this paper is to study a kind of complete convergence for weighted sums of pairwise negatively quadrant dependent (NQD) sequences with EX=0,E|X|exp(lnα|X|)<∞,α>1.By applying moment inequality and truncation methods, the sufficient conditions of complete convergence theorem of weighted sums for arrays of row-wise pairwise NDQ random variables are established, which extends to the case of weighted sums of pairwise negatively quadrant dependent sequences with imposing weighted condition. Our results generalize corresponding result obtained by WU et al.
Key words: arrays with row-wise pairwise negatively quadrant dependent sequences    weighted sums    complete convergence
收稿日期: 2016-10-06 出版日期: 2017-05-01
CLC:  O211.4  
作者简介: 章茜(1984-),ORCID:http://orcid.org/0000-0002-2955-4600,女,硕士,讲师,主要从事概率极限理论研究,E-mail:qiwa_007@163.com.
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引用本文:

章茜. 行为两两NQD随机变量阵列加权和的完全收敛性[J]. 浙江大学学报（理学版）, 2017, 44(5): 538-541.

ZHANG Qian. Complete convergence for weighted sums of arrays with row-wise pairwise negatively quadrant dependent sequences. Journal of ZheJIang University(Science Edition), 2017, 44(5): 538-541.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.05.007    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I5/538

[1] LEHMAMN E L. Some concepts of dependence[J]. Ann Math Stat,1966,37:1137-1153.
[2] JOAG-DEVK, PROSCHAN F. Negative association of random variables with applications[J]. Ann-Statist,1983(11):286-295.
[3] 吴群英.两两NQD列的收敛性质[J].数学学报,2002,45(3):617-624. WU Q Y. Convergence properties of pairwise NQD random sequences[J]. Acta Mathematica Sinica,2002,45(3):617-624.
[4] 陈平炎.两两NQD随机序列的Lr收敛性[J].数学物理学报:A辑,2008,28(3):447-453. CHEN P Y. Lrconvergence for pairwise NQD random variables[J]. Acta Mathematica Scientia:SerA,2008,28(3):447-453.
[5] 方炜,郭明乐.行为两两NQD阵列加权和的矩完全收敛性[J].工程数学学报,2013,30(5):761-772. FANG W, GUO M L. Complete moment convergence of weighted sums for arrays of row-wise pairwise NQD random variables[J].Chinese Journal of Engineering Mathematics,2013,30(5):761-772.
[6] 邱德华,甘师信.两两NQD列随机变量序列的完全收敛性[J].武汉大学学报:理学版,2013,59(3):285-290. QIU D H, GAN S X. Complete convergence for sequence of pairwise NQD random variables[J]. Journal of Wuhan University:Natural Sciences Edition,2013,59(3):285-290.
[7] MI-HWA K. On Complete convergence for weighted sums of pairwise negatively quadrant dependent sequences[J]. Communications of Korean Statistical Society,2012,19(2):247-256.
[8] GUT A, STADTMULLER U. An intermediate Baum-Katz theorem[J]. Statist Probab Lett,2011(10):1486-1492.
[9] WU Q Y, JIANG Y Y. Complete convergence and complete moment convergence for negatively associated sequences of random variables[J]. Journal of Inequalities and Applications,2016(1):1-10.
[10] LI D L, RAO M B, WANG X C. Complete convergence of moving average processes[J]. Statist Probab Lett,1992(14):111-114.
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