• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.379-392
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• 2013

A general result for the complete convergence of arrays of rowwise extended negatively dependent random variables is derived. As its applications eight corollaries for complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables are given, which extend the corresponding known results for independent case.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1007-1025
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• 2019

In the present work, the complete convergence and complete moment convergence properties for arrays of rowwise extended negatively dependent (END) random variables are investigated. Some sharp theorems on these strong convergence for weighted sums of END cases are established. These main results not only generalize the known corresponding ones of Cai [2], Wang et al. [17] and Shen [14], but also improve them, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.507-519
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• 2012

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.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1097-1110
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• 2012

The convergence properties of extended negatively dependent sequences under some conditions of uniform integrability are studied. Some sufficient conditions of the weak law of large numbers, the $p$-mean convergence and the complete convergence for extended negatively dependent sequences are obtained, which extend and enrich the known results in the literature.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1485-1508
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• 2020

In this paper, we investigate the complete f-moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete f-moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.

• 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.

• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.21-33
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• 2005

Let ｛X/sun ni/ ｜ 1 ≤ i ≤ n, n ≥ 1 ｝ be an array of rowwise negatively associated random variables. We in this paper discuss the conditions of n/sup -1/p/ (equation omitted) →0 completely as n → ∞ for some 1 ≤ p < 2 under not necessarily identically distributed setting. As application, it is obtained that n/sup -1/p/ (equation omitted) →0 completely as n → ∞ if and only if E｜X/sub 11/｜/sup 2p/ < ∞ and EX/sub ni=0 under identically distributed case such that the corresponding results on i. i. d. case are extended and the strong convergence for weighted sums of rowwise negatively associated arrays is also considered.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.897-907
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• 2017

In this paper, we consider the strong stability of a type of Jamison weighted sums, which not only extend the corresponding result of Jamison etc. [13] from i.i.d. case to END random variables, but also obtain the necessary and sufficient results. As an important consequence, we present the result of SLLN as that of i.i.d. case.