Weak and Strong Laws of Large Numbers of Negatively Associated Random Variables

Date
2017-04
Authors
Atkinson, Christopher Mark
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Publisher
Faculty of Graduate Studies and Research, University of Regina
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.

Description
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. v, 154 p.
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