Negatively dependent bounded random variable probability inequalities and the strong law of large numbers

M. Amini and A. Bozorgnia

International Journal of Stochastic Analysis, 2000, vol. 13, 1-7

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 .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:606935

DOI: 10.1155/S104895330000023X

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