Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES

  • SEO, HYE-YOUNG (School of Big Data &Financiall Statistics, and Institute of Basic Natural Science, Wonkwang University) ;
  • SHII, DA-LI (Graduate School, Wonkwang University) ;
  • BAEK, JONG-IL (School of Big Data &Financiall Statistics, and Institute of Basic Natural Science, Wonkwang University)
  • Received : 2019.01.03
  • Accepted : 2019.03.21
  • Published : 2019.05.30
Download PDF
⟨ Previous Next ⟩

Abstract

We are presented of several basic properties for negatively superadditive dependent(NSD) random variables. By using this concept we are obtained complete convergence for maximum partial sums of rowwise NSD random variables. These results obtained in this paper generalize a corresponding ones for independent random variables and negatively associated random variables.

Keywords

Acknowledgement

Supported by : Wonkwang University

References

  1. K. Alam and K.M.L. Saxena, Positive dependence in multivariate distributions, Comm. Stati. Theor. Method A10 (1981), 1183-1196.
  2. H.W. Block,, T.H.Savits and M.Shaked, Some concepts of negative dependence, Ann. Probability 10 (1982), 765-772. https://doi.org/10.1214/aop/1176993784
  3. H.Y. Seo, J.I. Baek, On Hajek-Renyi-Thype inequality for conditionally negatively associated random variables and its applications, J. Appl. Math. & Informatics 30 (2012), 623-633. https://doi.org/10.14317/JAMI.2012.30.3_4.623
  4. T.C. Christofides and E. Vaggelatou, A connection between supermodular ordering and positive/negative association, J. Mult. Analysis 88 (2004), 138-151. https://doi.org/10.1016/S0047-259X(03)00064-2
  5. D.K. Fuk and S.V. Nagaev, Probability inequalities for sums of independent random variables, Theor. Probab. Apple 16 (1971), 643-660. https://doi.org/10.1137/1116071
  6. K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statistics 11 (1983), 286-295. https://doi.org/10.1214/aos/1176346079
  7. T.Z. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probability and Statistics 16 (2000), 133-144. https://doi.org/10.3969/j.issn.1001-4268.2000.02.003