Negatively Dependent Bounded Random Variable Probability Inequalities and the Strong Law of Large Numbers

@inproceedings{Amini2000NegativelyDB,
title={Negatively Dependent Bounded Random Variable Probability Inequalities and the Strong Law of Large Numbers},
author={Massoud Amini and Arezoo Bozorgnia},
year={2000}
}

be negatively dependent uniformly bounded random variables with d.f. F(x). In this paperwe obtain bounds for the^ probabilities P(I Y=IXil >_nt) and P(l(pn-pl >e) where pn is the sample pth ^quantile and p is the pth quantile of F(x). Moreover, we show that pn is a strongly consistent estimator of p under mild^ restrictions on F(x) in the neighborhood of p. We also show that (pn converges completely to p.