Weak and Strong Laws of Large Numbers of Negatively Associated Random Variables
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Abstract
In this thesis, the purpose is to investigate the assumptions which are applicable for negative associated random variables to satisfy the weak and strong laws of large numbers. Additionally, sharp exponential inequalities are proved for maximum of sums of bounded and unbounded M-acceptable and negative associated random variables. Regarding the weak law of large numbers, it is proved that the weak law of large numbers is true for negative associated random variables as soon as the weak law is satis ed by independent random variables with identical marginal distributions. Also, the criterion for the weak law of large numbers for maximum of sums of negative associated random variables is obtained. Regarding the strong law, we proved the strong law of large numbers exists with di ering levels of generality in the criteria. It was found that many criterions for the strong law of large numbers for independent random variables are applicable for negative associated random variables.