Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE STRONG LAWS OF LARGE NUMBERS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES

  • Baek, J.I. (School of Mathematical Science and institute of Basic Natural Science, WonKwang University) ;
  • Choi, J.Y. (School of Mathematical Science and institute of Basic Natural Science, WonKwang University) ;
  • Ryu, D.H. (Department of Computer Science, ChungWoon University)
  • Published : 2004.05.01

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Abstract

Let{$X_{ni}$\mid$\;1\;{\leq}\;i\;{\leq}\;k_n,\;n\;{\geq}\;1$} be an array of rowwise negatively associated random variables such that $P$\mid$X_{ni}$\mid$\;>\;x)\;=\;O(1)P($\mid$X$\mid$\;>\;x)$ for all $x\;{\geq}\;0,\;and\; \{k_n\}\;and\;\{r_n\}$ be two sequences such that $r_n\;{\geq}\;b_1n^r,\;k_n\;{\leq}\;b_2n^k$ for some $b_1,\;b_2,\;r,\;k\;>\;0$. Then it is shown that $\frac{1}{r_n}\;max_1$\mid${\Sigma_{i=1}}^j\;X_{ni}$\mid$\;{\rightarrow}\;0$ completely convergence and the strong convergence for weighted sums of N A arrays is also considered.

Keywords

References

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