TAILIEUCHUNG - Báo cáo hóa học: " Probability inequalities for END sequence and their applications"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Probability inequalities for END sequence and their applications | Shen Journal of Inequalities and Applications 2011 2011 98 http content 2011 1 98 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Probability inequalities for END sequence and their applications Aiting Shen Correspondence baret@ School of Mathematical Science Anhui University Hefei 230039 PR China Springer Abstract Some probability inequalities for extended negatively dependent END sequence are provided. Using the probability inequalities we present some moment inequalities especially the Rosenthal-type inequality for END sequence. At last we study the asymptotic approximation of inverse moment for nonnegative END sequence with finite first moments which generalizes and improves the corresponding results of Wu et al. Stat. Probab. Lett. 79 1366-1371 2009 Wang et al. Stat. Probab. Lett. 80 452-461 2010 and Sung J. Inequal. Appl. 2010 Article ID 823767 13pp. 2010 . doi 2010 823767 . MSC 2000 60E15 62G20. Keywords extended negatively dependent sequence probability inequality moment inequality inverse moment 1 Introduction It is well known that the probability inequality plays an important role in various proofs of limit theorems. In particular it provides a measure of convergence rate for the strong law of large numbers. The main purpose of the article is to provide some probability inequalities for extended negatively dependent END sequence which contains independent sequence NA sequence and NOD sequence as special cases. These probability inequalities for END random variables are mainly inspired by Fakoor and Azarnoosh 1 and Asadian et al. 2 . Using the probability inequalities we can further study the moment inequalities and asymptotic approximation of inverse moment for END sequence. First we will recall the definitions of NOD and END sequences. Definition cf. Joag-Dev and Proschan 3 . A finite collection of random variables X1 X2 . Xn is said to be negatively .

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