• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.755-768
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• 1997

In this paper we introduce a new concept of negative dependence of multivariate random variables. This concept is weaker than the negative orthant dependence(NOD) but it enjoys some properties and preservation results of NOD.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.393-405
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• 2011

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 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.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.117-127
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• 2003

In this note we perform an extreme point analysis on two natural definitions of negative quadrant dependence of three random variables and examine how different these two notions of dependence. We also characterize some special distributions which are both negatively lower orthant dependent and negatively upper orthant dependent.

• Communications for Statistical Applications and Methods
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• v.5 no.1
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• pp.193-203
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• 1998

In this paper, we introduce a new concept of the multivariate positive dependence. This concept is weaker than the positive orthant dependence. Some basic properties and preservation results are presented.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.847-858
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• 1997

In this note we develop a partial ordering among positive lower orthant dependent distributions with fixed marginals. This permits us to measure the degree of positive lower orthant dependence. Some basic properties and preservation results are derived.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.75-83
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• 2011

In this paper the Baum-Katz law of large numbers for negatively orthant dependent random variables is studied. The complete convergence of negatively orthant dependent random variables under some conditions of uniform integrablity is also obtained.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1059-1068
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• 2000

In this paper we introduce a new concept of weakly positive upper orthant dependence POD of hitting times of stochastic processes. This concept is weaker than the positively orthant dependent and it is closed under a certain statistical operations of W POD ordering. Examples are given to illustrate these concepts.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.223-238
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• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.649-662
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• 1999

A random vector =(X1,…, Xn) is conditionally weakly associated if and only if for every pair of partitions 1=(X$\pi$(k+1),…,X$\pi$(k)), 2=(X$\pi$(k+1),…,X$\pi$(n)) of P(1$\in$A│2$\in$B, $\theta$$\in$I) $\geq$P$\in$A│$\theta$$\in$I whenever A and B are open upper sets and $\pi$ is any permutation of {1,…,n}. In this note we develop some concepts of conditional positive dependence, which are weaker than conditional weak association but stronger than conditional positive orthant dependence, by requiring the above inequality to hold only for some upper sets and applying the arguments in Shaked (1982).