DOI QR코드

DOI QR Code

THE COMPLETE MOMENT CONVERGENCE FOR ARRAY OF ROWWISE ENOD RANDOM VARIABLES

  • Ryu, Dae-Hee (Department of Computer Science, ChungWoon University)
  • Received : 2011.07.25
  • Accepted : 2011.08.15
  • Published : 2011.09.25

Abstract

In this paper we obtain the complete moment convergence for an array of rowwise extended negative orthant dependent random variables. By using the result we can prove the complete moment convergence for some positively orthant dependent sequence satisfying the extended negative orthant dependence.

Keywords

References

  1. Ebrahimi, N. and Ghosh, M.(1981) Multivariate negative dependence, Commun, Statist Theor. Meth. 10 307-337 https://doi.org/10.1080/03610928108828041
  2. Chow, Y.S.(1988) On the rate of moment complete convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16 177-201
  3. Fuk, D.K. and Nagaev, S.V.(1971) Probability inequalities for sums of independent random variables, Theor. Probab. Apple. 16 643-660 https://doi.org/10.1137/1116071
  4. Hsu, P.L. and Robbins, H.(1947) Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 25-31 https://doi.org/10.1073/pnas.33.2.25
  5. Joag-Dev, K. and Proschan, F.(1983) Negative association of random variables with applications, Ann. Statist. 11 286-295 https://doi.org/10.1214/aos/1176346079
  6. Liu, L.(2009) Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Letts. 99 1290-1298
  7. Wang, D.C. and Zhao, W.(2006) Moment complete convergence for sums of a sequence NA random variables, Appl. Math. J. Chinese Univ. 21 445-450(in Chinese)
  8. Zhu, M.H.(2007) Strong laws of large numbers for arrays of rowwise ${\rho}^*$-mixing random variables, Discrete Dynamics in Nature Soc. Vol. 2007 Article ID 74296, 6 pages 2007