ON THE STRONG LAW OF LARGE NUMBERS FOR SEQUENCES OF PAIRWISE NEGATIVE QUADRANT DEPENDENT RANDOM VARIABLES

被引：0

作者：

Li, Deli ^{[1
]}

Rosalsky, Andrew ^{[2
]}

Volodin, Andrei I. ^{[3
]}

机构：

[1] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

[2] Univ Florida, Dept Stat, Gainesville, FL 32611 USA

[3] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

来源：

BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES | 2006年 / 1卷 / 02期

关键词：

Almost certain convergence; Sequence of pairwise negative quadrant dependent random variables; strong law of large numbers; weighted sums;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a sequence of pairwise negative quadrant dependent random variables {X-n, n >= 1}, conditions are given under which normed and centered partial sums converge to 0 almost certainly. As special cases, new results are obtained for weighted sums {Sigma(n)(j-1) a(j)X(j), n >= 1} where {a(n), n >= 1} is a sequence of positive constants and the {X-n, n >= 1} are also identically distributed. A result of Matula [19] is obtained by taking an equivalent to 1. Moreover, it is shown that a pairwise negative quadrant dependent sequence (which is not a sequence of independent random variables) can be constructed having any specified continuous marginal distributions. Illustrative examples are provided, two of which show that the pairwise negative quadrant dependence assumption cannot be dispensed with.

引用

页码：281 / 305

页数：25

共 27 条

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