The Hà jek-Rènyi-type inequality for associated random variables

A Hàjek-Rènyi-type inequality for associated random variables was obtained by Prakasa Rao [Prakasa Rao, B.L.S., 2002. Hàjek-Rènyi-type inequality for associated sequences. Statist. Probab. Lett. 57, 139-143]. Recently, Sung [Sung, H.S., 2008. A note on the Hàjek-Rènyi inequality for associated random variables. Statist. Probab. Lett. 78, 885-889] improved the inequality of Prakasa Rao in the above-mentioned reference. In the paper, we use different methods from Sung's and improve the results of Sung in the second reference cited above.