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On the Probability Inequalities under Linearly Negatively Quadrant Dependent Condition

  • Baek, Jong Il (School of Mathematics & Informational Statistics and Institute of Basic Natural Science, Wonkwang University) ;
  • Choi, In Bong (School of Mathematics & Informational Statistics and Institute of Basic Natural Science, Wonkwang University) ;
  • Lee, Seung Woo (School of Mathematics & Informational Statistics and Institute of Basic Natural Science, Wonkwang University)
  • Published : 2003.08.01

Abstract

Let X$_1$, X$_2$, … be real valued random variables under linearly negatively quadrant dependent (LNQD). In this paper, we discuss the probability inequality of ennett(1962) and Hoeffding(1963) under some suitable random variables. These results are to extend Theorem A and B to LNQD random variables. Furthermore, let ζdenote the pth quantile of the marginal distribution function of the $X_i$'s which is estimated by a smooth estima te $ζ_{pn}$, on the basis of X$_1$, X$_2$, …$X_n$. We establish a convergence of $ζ_{pn}$, under Hoeffding-type probability inequality of LNQD.

Keywords

References

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