Complete convergence for weighted sums of negatively associated random variables

2000 ◽  
Vol 48 (4) ◽  
pp. 317-325 ◽  
Author(s):  
Han-Ying Liang
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

scholarly journals Complete Convergence for Arrays of Rowwise Asymptotically Almost Negatively Associated Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Xuejun Wang ◽  
Shuhe Hu ◽  
Wenzhi Yang
Keyword(s):  
Complete Convergence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Weighted Sums ◽  
Strong Law ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables ◽  
Large Numbers ◽  
Asymptotically Almost Negatively Associated

Let{Xni,i≥1,n≥1}be an array of rowwise asymptotically almost negatively associated random variables. Some sufficient conditions for complete convergence for arrays of rowwise asymptotically almost negatively associated random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of asymptotically almost negatively associated random variables is obtained.

scholarly journals Complete Convergence for Maximal Sums of Negatively Associated Random Variables

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Victor M. Kruglov
Keyword(s):  
Complete Convergence ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Maximal Inequalities ◽  
Negatively Associated Random Variables ◽  
Necessary And Sufficient

Necessary and sufficient conditions are given for the complete convergence of maximal sums of identically distributed negatively associated random variables. The conditions are expressed in terms of integrability of random variables. Proofs are based on new maximal inequalities for sums of bounded negatively associated random variables.

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