Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 261-267
Negatively dependent bounded random variable probability
inequalities and the strong law of large numbers
Ferdowsi University, Faculty of Mathematical Sciences, Mashhad, Iran
Received 1 January 1998; Revised 1 January 2000
Copyright © 2000 M. Amini and A. Bozorgnia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be negatively dependent uniformly bounded random
variables with d.f. . In this paper we obtain bounds for the probabilities and where is the
sample th quantile and is the th quantile of . Moreover, we
show that is a strongly consistent estimator of under mild
restrictions on in the neighborhood of . We also show that
converges completely to .