Abstract
The classical theorem concerns the arithmetic means which is a regular method of summability. In this paper, under a large class of summability methods, a result for strong law of large numbers for negatively associated random variables is obtained. To investigate this result, this paper establishes a moment inequality for negatively associated random variables. Then, by restricting the moment conditions and use the method of summability, the result is extended for negatively associated random variables, which is closely related to classical theorems. Namely, it links in some sense the strong law of large numbers of Kolmogorov and that of Marcinkiewicz.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Joag-Dev, K., Proschan, F.: Negative association of random variables with applications. Ann. Statistic. 11, 286–295 (1983)
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)Â 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)
Jajte, R.: On the strong law of large numbers. Ann. Probab. 31(01), 409–412 (2003)
Kuczmaszewska, A.: The strong law large numbers for dependent random variables. Statis. Probab. Lett. 73, 305–314 (2005)
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)
Xing, G.D.: On the exponential inequalities for strictly stationary and negatively associated random variables. Journal of Statistical Planning and Inference 139(10) (2009)
Révész, P.: The Laws of Large Numbers. Academic Press (1968)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, Y., Tan, Y., Liu, Y. (2011). Strong Law of Large Numbers for Negatively Associated Random Variables. In: Liu, C., Chang, J., Yang, A. (eds) Information Computing and Applications. ICICA 2011. Communications in Computer and Information Science, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27452-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-27452-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27451-0
Online ISBN: 978-3-642-27452-7
eBook Packages: Computer ScienceComputer Science (R0)