Skip to main content
SpringerLink
Log in

The strong law of large numbers for pairwise NQD random variables

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992) and Wu (2001) from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. L. Lehmann, Some concepts of dependence, Ann. Math. Statist., 1966, 43: 1137–1153.

    Article  MathSciNet  Google Scholar 

  2. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 1983, 11(1): 286–295.

    Article  MathSciNet  Google Scholar 

  3. P. A. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett., 1992, 15: 209–213.

    Article  MATH  MathSciNet  Google Scholar 

  4. Y. B. Wang, C. Su, and X. G. Lin, On some limit properties for pairwise NQD sequences, Acta Mathematicae Applicatea Sinica., 1998, 21(3): 404–414.

    MATH  Google Scholar 

  5. Q. Y. Wu, Strong convergence properties of Jamison weighted sums of pairwise NQD random sequences, Journal of Mathematical Study, 2001, 34(4): 386–393.

    MATH  MathSciNet  Google Scholar 

  6. Q. Y. Wu, Convergence properties of pairwise NQD random sequences, Acta Mathematica Sinica., 2002, 45(3): 617–624.

    MATH  MathSciNet  Google Scholar 

  7. Y. X. Li and J. F. Wang, An application of Stein’s method to limit theorems for pairwise negative quadrant dependent random variables, Metrika, 2008, 67(1): 1–10.

    Article  MathSciNet  Google Scholar 

  8. Marcinkiewicz, Zygmund, Sur les functions independents, Fund Math., 1937, 29: 60–90.

    Google Scholar 

  9. B. Jamison, Convergence of weighted of independent random variables, Z. Wahrsch Verb Gebiete., 1965, 4: 40–44.

    Article  MATH  MathSciNet  Google Scholar 

  10. T. K. Chandra and A. Goswami, Cesaro uniform integrability and the strong law of number, Sankhya., 1992, 54(2): 215–231.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Guilin University of Technology, Guilin, 541004, China

    Qunying Wu & Yuanying Jiang

Authors
  1. Qunying Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanying Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qunying Wu.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 11061012, the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 2010GXNSFA013120.

This paper was recommended for publication by Editor Guohua ZOU.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Q., Jiang, Y. The strong law of large numbers for pairwise NQD random variables. J Syst Sci Complex 24, 347–357 (2011). https://doi.org/10.1007/s11424-011-8086-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-011-8086-4

Key words

Search

Navigation