Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A WEAK LAW FOR WEIGHTED SUMS OF ARRAY OF ROW NA RANDOM VARIABLES

  • Baek, Jong-Il (School of Mathematics & Informational Statistics, and Institute of Basic Natural Sciences, Wonkwang University) ;
  • Liang, Han-Ying (Department of Applied Mathematics, Tongji University) ;
  • Choi, Jeong-Yeol (School of Mathematics & Informational Statistics, and Institute of Basic Natural Sciences, Wonkwang University)
  • Published : 2003.05.01
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Abstract

Let {$x_{nk}\;$\mid$1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$} be an array of random varianbles and $\{a_n$\mid$n\;\geq\;1\}\;and\;\{b_n$\mid$n\;\geq\;1} be a sequence of constants with $a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (${\sum_{\kappa=1}}^n\;a_{\kappa}X_{n\kappa}\;-\;\nu_{n\kappa})\;/b_n$ converges in probability to zero, as $n\;\rightarrow\;\infty$, where {$\nu_{n\kappa}$\mid$1\;\leq\;\kappa\;\leq\;n,\;n\;\geq\;1$} is a suitable array of constants.

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