Exponential inequalities and inverse moment for NOD sequence

Some exponential inequalities for a negatively orthant dependent sequence are obtained. By using the exponential inequalities, we study the asymptotic approximation of inverse moment for negatively orthant dependent random variables, which generalizes and improves the corresponding results of Kaluszka and Okolewski [Kaluszka, M., Okolewski, A., 2004. On Fatou-type lemma for monotone moments of weakly convergent random variables. Statist. Probab. Lett. 66, 45-50], Hu et al. [Hu, S.H., Chen, G.J., Wang, X.J., Chen, E.B., 2007. On inverse moments of nonnegative weakly convergent random variables. Acta Math. Appl. Sin. 30, 361-367(in Chinese)] and Wu et al. [Wu, T.J., Shi, X.P., Miao, B.Q., 2009. Asymptotic approximation of inverse moments of nonnegative random variables. Statist. Probab. Lett. 79, 1366-1371].