# THE WEAK LAW OF LARGE NUMBER FOR NORMED WEIGHTED SUMS OF STOCHASTICALLY DOMINATED AND PAIRWISE NEGATIVELY QUADRANT DEPENDENT RANDOM VARIABLES

• KIM, TAE-SUNG (Division of Mathematics, Wonkwang University) ;
• CHOI, JEONG-YEOL (Division of Mathematics, Wonkwang University) ;
• KIM, HYUN-CHUL (Division of Computer Science, Daebull University)
• Published : 1999.07.30
• 38 1

#### Abstract

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form$({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$is established, where$\{{\nu}_n,\;n{\geq}1\}\$ is a suitable sequence.

#### Keywords

stochastically dominated;negatively quadrant dependent;weak law of large number;normed weighted sum

#### Acknowledgement

Supported by : Wonkwang University

#### References

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