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Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables

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  • Qunying Wu

Abstract

The complete convergence for pairwise negative quadrant dependent (PNQD) random variables is studied. So far there has not been the general moment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. Sufficient and necessary conditions of complete convergence for weighted sums of PNQD random variables are obtained. Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).

Suggested Citation

  • Qunying Wu, 2012. "Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:104390
    DOI: 10.1155/2012/104390
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    References listed on IDEAS

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    1. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
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    Cited by:

    1. Aiting Shen, 2013. "On Strong Convergence for Weighted Sums of a Class of Random Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Qunying Wu & Yuanying Jiang, 2016. "Complete Moment Convergence for Negatively Dependent Sequences of Random Variables," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-6, July.

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