Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 58317, 8 pages
doi:10.1155/JIA/2006/58317

Hajek-Renyi-type inequality for some nonmonotonic functions of associated random variables

Isha Dewan1 and B. L. S. Prakasa Rao2

 1Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi 110016, India
2Department of Mathematics and Statistics, University of Hyderabad, Hyderabad 500046, India
Received 21 April 2005; Revised 26 October 2005; Accepted 11 December 2005

Abstract

Let {Yn,n≥1} be a sequence of nonmonotonic functions of associated random variables. We derive a Newman and Wright (1981) type of inequality for the maximum of partial sums of the sequence {Yn,n≥1} and a Hajek-Renyi-type inequality for nonmonotonic functions of associated random variables under some conditions. As an application, a strong law of large numbers is obtained for nonmonotonic functions of associated random varaibles.