• Title, Summary, Keyword: strong law

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The Strong Laws of Large Numbers for Weighted Averages of Dependent Random Variables

  • Kim, Tae-Sung;Lee, Il-Hyun;Ko, Mi-Hwa
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.451-457
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    • 2002
  • We derive the strong laws of large numbers for weighted averages of partial sums of random variables which are either associated or negatively associated. Our theorems extend and generalize strong law of large numbers for weighted sums of associated and negatively associated random variables of Matula(1996; Probab. Math. Statist. 16) and some results in Birkel(1989; Statist. Probab. Lett. 7) and Matula (1992; Statist. Probab. Lett. 15 ).

STRONG LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Ko, Mi-Hwa;Han, Kwang-Hee;Kim, Tae-Sung
    • Journal of the Korean Mathematical Society
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    • v.43 no.6
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    • pp.1325-1338
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    • 2006
  • For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences of negatively orthant dependent random variables ${X_n,\;n{\geq}1}$, the conditions for strong law of large number of ${\sum}^{k_n}_{i=1}a_{ni}X_i$ are given. Both cases $k_n{\uparrow}{\infty}\;and\;k_n={\infty}$ are treated.

MAXIMAL INEQUALITIES AND STRONG LAW OF LARGE NUMBERS FOR AANA SEQUENCES

  • Xuejun, Wang;Shuhe, Hu;Xiaoqin, Li;Wenzhi, Yang
    • Communications of the Korean Mathematical Society
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    • v.26 no.1
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    • pp.151-161
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    • 2011
  • Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

On the Strong Law of Large Numbers for Convex Tight Fuzzy Random Variables

  • Joo Sang Yeol;Lee Seung Soo
    • Proceedings of the Korean Statistical Society Conference
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    • pp.137-141
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    • 2001
  • We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).

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On the strong law of large numbers for pairwise negative quadrant dependent random variables

  • T. S.;J. I.;H. Y.
    • Communications for Statistical Applications and Methods
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    • v.7 no.1
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    • pp.291-296
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    • 2000
  • Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

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