• Title, Summary, Keyword: Weighted sums

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Convergence in Probability for Weighted Sums of Fuzzy Random Variables

  • Joo, Sang-Yeol;Hyun, Young-Nam
    • Communications for Statistical Applications and Methods
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    • v.12 no.2
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    • pp.275-283
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    • 2005
  • In this paper, we give a sufficient condition for convergence in probability of weighted sums of convex-compactly uniformly integrable fuzzy random variables. As a result, we obtain weak law of large numbers for weighted sums of convexly tight fuzzy random variables.

THE STRONG LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF PAIRWISE QUADRANT DEPENDENT RANDOM VARIABLES

  • Kim, Tae-Sung;Baek, Jong-Il
    • Journal of the Korean Mathematical Society
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    • v.36 no.1
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    • pp.37-49
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    • 1999
  • We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

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ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF 2-DIMENSIONAL ARRAYS OF POSITIVE DEPENDENT RANDOM VARIABLES

  • Kim, Tae-Sung;Baek, Ho-Yu;Han, Kwang-Hee
    • Communications of the Korean Mathematical Society
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    • v.14 no.4
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    • pp.797-804
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    • 1999
  • In this paper we derive the almost sure convergence of weighted sums of 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our re-sults imply and extension of Etemadi's(1983) strong laws of large numbers for weighted sums of nonnegative random variables to the 2-dimensional case.

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STRONG CONVERGENCE FOR WEIGHTED SUMS OF FUZZY RANDOM VARIABLES

  • Kim, Yun-Kyong
    • Proceedings of the Korean Statistical Society Conference
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    • pp.183-188
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    • 2003
  • In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

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STRONG LAWS FOR WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES

  • Cai, Guang-Hui
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.771-778
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    • 2006
  • Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ([12]).