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)
  • Received : 1999.04.26
  • Published : 1999.07.30

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

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