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An exponential inequality for a NOD sequence and a strong law of large numbers. (English) Zbl 1205.60068
Summary: We establish an exponential inequality for unbounded negatively orthant dependent (NOD) random variables. The inequality extends and improves the results of T. S. Kim and H. C. Kim [Commun. Korean Math. Soc. 22, No. 2, 315–321(2007; Zbl 1168.60335)], H. J. Nooghabi and H. A. Azarnoosh [Stat. Pap. 50, No. 2, 419–428 (2009; Zbl 05603774)], and G. D. Xing, S. C. Yang, A. L. Liu and X. P. Wang, J. Korean Stat. Soc. 38, No. 1, 53–57 (2009)]. We also obtain the convergence rate $O\left({n}^{-1/2}{ln}^{1/2}n\right)$ for the strong law of large numbers, which improves on the corresponding ones of Kim and Kim [loc. cit.], Nooghabi and Azarnoosh (2009), and Xing, Yang, Liu and Wang [loc. cit.].
##### MSC:
 60F15 Strong limit theorems