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:10.1155/2010/823767]. MSC(2000): 60E15; 62G20.
Highlights
It is well known that the probability inequality plays an important role in various proofs of limit theorems
We present some moment inequalities, especially the Rosenthal-type inequality for extended negatively dependent (END) sequence
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
Summary
It is well known that the probability inequality plays an important role in various proofs of limit theorems. 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]. A finite collection of random variables X1, X2, ..., Xn is said to be negatively orthant dependent (NOD) if they are both NUOD and NLOD. Throughout the article, let {Xn, n ≥ 1} be a sequence of END random variables defined on a fixed probability space ( , F , P) with respective distribution functions F1, F2,.
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