Abstract
In this work, the complete moment convergence and Lp convergence for asymptotically almost negatively associated (AANA, in short) random variables are investigated. As an application, the complete convergence theorem for weighted sums of AANA random variables is obtained. These theorems obtained extend and improve some earlier results.
Highlights
Definition 1.1 A finite collection of random variables X1, X 2,..., X n is said to be negatively associated (NA, in short) if for every pair of disjoint subsets A1 and A2 of {1, 2,..., n},( ( )) Cov f1 ( Xi : i ∈ A1 ), f2 X j : i ∈ A2 ≤ 0 (1.1)whenever f1 and f2 are any real coordinatewise nondecreasing functions such that this covariance exists.An infinite sequence {X n ; n ≥ 1} of random variables is said to be NA if for every finite sub-collection is NA
The concept of NA was introduced by Joag-Dev and Proschan [4], and its probability limit properties have aroused wide interest because of their numerous applications in reliability theory, percolation theory and multivariate statistical analysis
Definition 1.2 A sequence {X n ; n ≥ 1} of random variables is called AANA if there exists a nonnegative sequence q (n) → 0 as n → ∞ such that
Summary
Definition 1.1 A finite collection of random variables X1, X 2 ,..., X n is said to be negatively associated (NA, in short) if for every pair of disjoint subsets A1 and A2 of. An infinite sequence {X n ; n ≥ 1} of random variables is said to be NA if for every finite sub-collection is NA. The concept of NA was introduced by Joag-Dev and Proschan [4], and its probability limit properties have aroused wide interest because of their numerous applications in reliability theory, percolation theory and multivariate statistical analysis. Definition 1.2 A sequence {X n ; n ≥ 1} of random variables is called AANA if there exists a nonnegative sequence q (n) → 0 as n → ∞ such that.
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