An exponential inequality for a NOD sequence and a strong law of large numbers

In this work, we establish an exponential inequality for unbounded negatively orthant dependent (NOD) random variables. The inequality extends and improves the results of Kim and Kim (2007) [1], Nooghabi and Azarnoosh (2009) [2], and Xing et al. (2009) [3]. We also obtain the convergence rate O ( n − 1 / 2 ln 1 / 2 n ) for the strong law of large numbers, which improves on the corresponding ones of Kim and Kim (2007) [1], Nooghabi and Azarnoosh (2009) [2], and Xing et al. (2009) [3].