On the Probability Inequalities under Linearly Negatively Quadrant Dependent Condition

Title & Authors
On the Probability Inequalities under Linearly Negatively Quadrant Dependent Condition
Baek, Jong Il; Choi, In Bong; Lee, Seung Woo;

Abstract
Let X$\small{_1}$, X$\small{_2}$, … 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 $\small{Ｘ_i}$'s which is estimated by a smooth estima te $\small{ζ_{pn}}$, on the basis of X$\small{_1}$, X$\small{_2}$, …$\small{X_n}$. We establish a convergence of $\small{ζ_{pn}}$, under Hoeffding-type probability inequality of LNQD.
Keywords
Linearly negatively quadrant dependent;Hoeffding-type probability Inequality;
Language
English
Cited by
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