Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON H$\grave{a}$JEK-R$\grave{e}$NYI-TYPE INEQUALITY FOR CONDITIONALLY NEGATIVELY ASSOCIATED RANDOM VARIABLES AND ITS APPLICATIONS

  • Seo, Hye-Young (School of Mathematic and Institute of Basic Natural Science, Wonkwang University) ;
  • Baek, Jong-Il (School of mathematics and Informational Statistics and Institute of Basic Natural Science, Wonkwang University)
  • Received : 2011.10.10
  • Accepted : 2012.02.03
  • Published : 2012.05.30
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Abstract

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n|n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_n|n{\geq}1$} is said to be conditionally negatively associated given $\mathcal{F}$ if for every pair of disjoint subsets A and B of {1, 2, ${\cdots}$, n}, $Cov^{\mathcal{F}}(f_1(X_i,i{\in}A),\;f_2(X_j,j{\in}B)){\leq}0$ a.s. whenever $f_1$ and $f_2$ are coordinatewise nondecreasing functions. We extend the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality from negative association to conditional negative association of random variables. In addition, some corollaries are given.

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References

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