Abstract
The classical complete convergence theorem concerns the arithmetic means which is a regular method of summability. In this paper, to obtain the main results, a new large class of summability methods is introduced. The results for complete convergence for negatively associated random variable sequence are obtained. To investigate this results, by restricting the moment conditions and use a new method of summability. Then the result of the complete convergence for NA random variables sequences are obtained by applying the Kolmogorov-type inequality for NA random variable sequence.
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References
Joag-Dev, K., Proschan, F.: Negative association of random variables with applications. Ann. Statistic. 11, 286–295 (1983)
Hsu, P.L., Robbins, H.: Complete convergence and the low of large numbers. Proc. Nat. Acad. Sci. USA 33, 25–31 (1947)
Shao, Q.-M., Su, C.: The Law of iterated logarithm for negatively associated random variables. Process. Appl. 83, 139–148 (1999)
Lin, Z., Lu, C., Su, Z.: Foundations of probability limit theory. College Mathematics Journal, 98–106 (1999)
Christofiders, T.C., Vaggelatou, E.: A connection between supermodular ordering and positive/negative association. Journal of Multivariate Analysis 88, 138–151 (2004)
Liu, L., Sheng, S.: On Sufficient and Necessary Condition of a Strong Law of Large Numbers for Negatively Associated Random Variables. Chinese Journal of Applied Probability and Statistics 24(4) (2008)
Zhou, S.-N., Ming, R.-X., Huang, L.: Complete Convergence for Randomly Weighted Sums of Negatively Associated Random Variables. Journal of Jiangxi Normal University (natural sciences edition), 33(6) (2009)
Liang, H., Zhang, J.: Strong Convergence for Weighted Sums of Negatively Associated Arrays. Chinese Annals of Mathematics, Series BÂ 31(2) (2010)
Xing, G., Yang, S.: Exponential Inequalities for Negatively Associated Random Variables. Acta Mathematica Scientia, 29(6) (2009)
Christofides, T.C., Hadjikyriakou, M.: Exponential inequalities for N-demimartingales and negatively associated random variables. Statistics & Probability Letters 79(19) (2009)
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Wang, Y., Liu, Y., Tan, Y. (2012). Complete Convergence for NA Random Sequence. In: Liu, C., Wang, L., Yang, A. (eds) Information Computing and Applications. ICICA 2012. Communications in Computer and Information Science, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34038-3_52
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DOI: https://doi.org/10.1007/978-3-642-34038-3_52
Publisher Name: Springer, Berlin, Heidelberg
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