• Title/Summary/Keyword: weighted sums

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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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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.

STRONG CONVERGENCE FOR WEIGHTED SUMS OF FUZZY RANDOM VARIABLES

  • Kim, Yun-Kyong
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.10a
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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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On Complete Convergence for Weighted Sums of Pairwise Negatively Quadrant Dependent Sequences

  • Ko, Mi-Hwa
    • Communications for Statistical Applications and Methods
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    • v.19 no.2
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    • pp.247-256
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    • 2012
  • In this paper we prove the complete convergence for weighted sums of pairwise negatively quadrant dependent random variables. Some results on identically distributed and negatively associated setting of Liang and Su (1999) are generalized and extended to the pairwise negative quadrant dependence case.

ON THE GENERAL QUADRATIC GAUSS SUMS WEIGHTED BY CHARACTER SUMS OVER A SHORT INTERVAL

  • Zhang, Tianping
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.873-883
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    • 2013
  • By using the analytic methods, the mean value of the general quadratic Gauss sums weighted by the first power mean of character sums over a short interval is investigated. Several sharp asymptotic formulae are obtained, which show that these sums enjoy good distributive properties. Moreover, interesting connections among them are established.