A note on the exponential inequality for a class of dependent random variables

An exponential inequality is established for a random variable with the finite Laplace transform. Using this inequality, we obtain an exponential inequality for identically distributed acceptable random variables (a class of random variables introduced in Giuliano Antonini, Kozachenko, and Volodin (2008) which includes negatively dependent random variables). Our result improves the corresponding ones in Kim and Kim (2007), Nooghabi and Azarnoosh (2009), Sung (2009), Xing (2009), Xing and Yang (2010) and Xing, Yang, Liu, and Wang (2009). Our method is much simpler than those in the literature.