Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ALMOST SURE CONVERGENCE FOR WEIGHTED SUMS OF NEGATIVELY ASSOCIATED RANDOM VARIABLES UNDER h-INTEGRABILITY

  • Ryu, Dae-Hee (Department of Computer Science, ChungWoon University) ;
  • Kim, Hyeock-Jin (Department of Computer Science, Chungwoon University)
  • Received : 2010.11.09
  • Accepted : 2010.12.24
  • Published : 2011.01.30
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Abstract

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

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References

  1. Billingsley, P. Convergence of Probability Measures, Wiley, New York (1968)
  2. Chandra, T. K. Uniform integrability in the Cesaaro sense and the weak law of large numbers, Sankhya Ser. A 51 (1989) 309-317
  3. Chandra, T. K. and Ghosal, S. Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar. 71 (1996) 327-336 https://doi.org/10.1007/BF00114421
  4. Joag-Dev, K. and Proschan, F. Negative association of random variables with applications. Ann. Statist. 11 (1983) 286-295 https://doi.org/10.1214/aos/1176346079
  5. Landers, D. and Rogge, L. Laws of large numbers for pairwise independent uniformly inte-grable random variables, Math. Nachr. 130 (1987) 189-192 https://doi.org/10.1002/mana.19871300117
  6. Lehmann,E.L. Some concepts of dependence, Ann. Math. Statist. 37 (1966) 1137-1153. https://doi.org/10.1214/aoms/1177699260
  7. Matula, P. A note on the almost sure convergence of sums of negatively dependent random variables. Statist. Prob. Lett. 15 (1992) 209-213 https://doi.org/10.1016/0167-7152(92)90191-7
  8. Ordonez Cabrera, M. Convergence of weighted sums of random variables and uniform inte- grability concerning the weights, Collect. Math. 45 (1994) 121-132
  9. Ordonez Cabrera, M. and Volodin, A. I. Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integraility, J. Math. Anal. Appl. 305 (2005) 644-658 https://doi.org/10.1016/j.jmaa.2004.12.025