Abstract
Let {X n , n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L p-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.
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Acknowledgements
The authors are very grateful to the referee for his/her valuable suggestions which improved the presentation of this work. This work is supported by NSFC (11001077), NCET (NCET-11-0945), HASTIT (2011HASTIT011), the Henan Province Foundation and Frontier Technology Research Plan (112300410205), and the Plan for Scientific Innovation Talent of Henan Province (124100510014).
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Miao, Y., Xu, W., Chen, S. et al. Some limit theorems for negatively associated random variables. Proc Math Sci 124, 447–456 (2014). https://doi.org/10.1007/s12044-014-0185-4
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DOI: https://doi.org/10.1007/s12044-014-0185-4
Keywords
- Negatively associated random variables
- L p-convergence
- Marcinkiewicz–Zygmund strong law of large numbers
- order statistics.