Abstract
In this article, applying moment inequality of negatively dependent (ND) random variables which obtained by Asadian et al., the complete convergence theorem for weighted sums of arrays of rowwise ND random variables is discussed. As a result, the complete convergence theorem for ND arrays of random variables is extended. Our results generalize and improve those on complete convergence theorem previously obtained by Hu et al., Ahmed et al, Volodin, and Sung from the independent and identically distributed case to ND sequences.Mathematical Subject Classification: 62F12.
Highlights
Random variables X and Y are said to be negatively dependent (ND) ifP(X ≤ x, Y ≤ y) ≤ P(X ≤ x)P(Y ≤ y) (1:1)for all x, y Î R
In this article we study the complete convergence for ND random variables
Our results generalize and improve those on complete convergence theorem previously obtained by Hu et al [16], Ahmed et al [15], Volodin [17] and Sung [18] from the i.i.d
Summary
Random variables X and Y are said to be negatively dependent (ND) ifP(X ≤ x, Y ≤ y) ≤ P(X ≤ x)P(Y ≤ y) (1:1)for all x, y Î R. 1 Introduction Random variables X and Y are said to be negatively dependent (ND) if The following definition is needed to define sequences of ND random variables.
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