Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T11:27:22.171Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES

Published online by Cambridge University Press:  29 November 2016

Qunying Wu  and
Yuanying Jiang
Qunying Wu
Affiliation:
College of Science, Guilin University of Technology, Guilin 541004, People's Republic of China E-mail: wqy666@glut.edu.cn
Yuanying Jiang
Affiliation:
College of Science, Guilin University of Technology, Guilin 541004, People's Republic of China E-mail: jyy@glut.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper, we study the almost sure convergence for sequences of asymptotically negative associated (ANA) random variables. As a result, we extend the classical Khintchine–Kolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem for sequences of independent random variables to sequences of ANA random variables without necessarily adding any extra conditions.

Keywords

applied probabilityoperations researchsimulationstochastic dynamic programming

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 1 , January 2018 , pp. 58 - 66
Copyright
Copyright © Cambridge University Press 2016 

References

1. Joag-Dev, K. & Proschan, F. (1983). Negative association of random variables with applications. Annals of Statistics 11(1): 286–295.Google Scholar
2. Kim, T.S., Ko, M.H., & Lee, I.H. (2004). On the strong laws for asymptotically almost negatively associated random variables. Rocky Mountain Journal of Mathematics 34: 979–988.Google Scholar
3. Ko, M.H. (2014). The Hájek–Rènyi inequality and strong law of large numbers for ANA random variables. Journal of Inequalities and Applications 2014: 521.CrossRefGoogle Scholar
4. Matula, P.A. (1992). A note on the almost sure convergence of sums of negatively dependent random variables. Statistics & Probability Letters 15: 209–213.Google Scholar
5. Wang, J.F. & Lu, F.B. (2006). Inequalities of maximum partial sums and weak convergence for a class of weak dependent random variables. Acta Mathematica Scientia English Series 23: 127–136.Google Scholar
6. Wang, J.F. & Zhang, L.X. (2007). A Berry–Esseen theorem and a law of the iterated logarithm for asymptotically negatively associated sequences. Acta Mathematica Scientia English Series 22: 693–700.Google Scholar
7. Wu, Q.Y. & Chen, P.Y. (2013). Strong representation results of Kaplan–Meier estimator for censored NA data. Journal of Inequalities and Applications 2013: 340.Google Scholar
8. Wu, Q.Y. & Chen, P.Y. (2013). A Berry–Esseen type bound in Kernel density estimation for negatively associated censored data. Journal of Applied Mathematics 2013: Article ID 541250, 9 page, http://dx.doi.org/10.1155/2013/541250.CrossRefGoogle Scholar
9. Yuan, D.M. & Wu, X.S. (2010). Limiting behavior of the maximum of the partial sum for asymptotically negatively associated random variables under residual Cesàro alpha-integrability assumption. Journal of Statistical Planning and Inference 140: 2395–2402.Google Scholar
10. Zhang, L.X. (2000). A functional central limit theorem for asymptotically negatively dependent random fields. Acta Mathematica Hungarica 86: 237–259.Google Scholar
11. Zhang, L.X. (2000). Central limit theorems for asymptotically negative dependent random field. Acta Mathematica Scientia English Series 16: 691–710.Google Scholar