Negatively dependent bounded random variable probability inequalities and the strong law of large numbers. (2000)

• Record Type: Journal Article
• Authors: Amini, M.; Bozorgnia, A.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 3(2000)
• Page Start: 261
• Page End: 267
• Publication Date: 2000
• Subjects: probability inequalities -- strong law of large numbers -- complete convergence; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895330000023X
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : Let X 1, …, X n be negatively dependent uniformly bounded random variables with d.f. F ( x ) . In this paper we obtain bounds for the probabilities P ( | ∑ i = 1 n X i | ≥ n t ) and P ( | ξ ˆ p n − ξ p | > ϵ ) where ξ ˆ p n is the sample p th quantile and ξ p is the p th quantile of F ( x ) . Moreover, we show that ξ ˆ p n is a strongly consistent estimator of ξ p under mild restrictions on F ( x ) in the neighborhood of ξ p . We also show that ξ ˆ p n converges completely to ξ p .