• 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.

• Journal of the Korean Statistical Society
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• v.12 no.1
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• pp.10-17
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• 1983

Let $X^{(n)}_j, j=1,2,\cdots,n, n=1,2,\cdots$ be a triangular array of random variables which arise naturally in a study of ferromagnetism in statistical mechanics. This paper presents weak convergence of random function $W_n(t)$, an appropriately normalized partial sum process based on $S^{(n)}_n = X^{(n)}_i+\cdot+X^{(n)}_n$. The limiting process W(t) is shown to be Gaussian when weak dependence exists. At the critical point where the change form weak to strong dependence takes place, W(t) turns out to be non-Gaussian. Our results are direct extensions of work by Ellis and Newmam (1978). An example is considered and the relation of these results to critical phenomena is briefly explained.

• Journal of The Korean Astronomical Society
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• v.47 no.1
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• pp.1-13
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• 2014

We analyze the dependence of disk morphology (arm class, Hubble type, bar type) of nearby spiral galaxies on the galaxy environment by using local background density (${\Sigma}_n$), projected distance ($r_p$), and tidal index (T I) as measures of the environment. There is a strong dependence of arm class and Hubble type on the galaxy environment, while the bar type exhibits a weak dependence with a high frequency of SB galaxies in high density regions. Grand design fractions and early-type fractions increase with increasing ${\Sigma}_n$, $1/r_p$, and T I, while fractions of flocculent spirals and late-type spirals decrease. Multiple-arm and intermediate-type spirals exhibit nearly constant fractions with weak trends similar to grand design and early-type spirals. While bar types show only a marginal dependence on ${\Sigma}_n$, they show a fairly clear dependence on $r_p$ with a high frequency of SB galaxies at small $r_p$. The arm class also exhibits a stronger correlation with $r_p$ than ${\Sigma}_n$ and T I, whereas the Hubble type exhibits similar correlations with ${\Sigma}_n$ and $r_p$. This suggests that the arm class is mostly affected by the nearest neighbor while the Hubble type is affected by the local densities contributed by neighboring galaxies as well as the nearest neighbor.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.269-273
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• 2003

We consider an efficient parametric estimation method of spatial dependence in weak stationary processes. Spatial dependence is modeled through variogram and correlogram. Most of parametric estimation methods of correlogram use two step method; nonparametric estimation and parametric integration. We bind these two steps into one step by using GEE method instead of least squares type optimization. Our one step method is more efficient statistically and gives a clear interpretation of related concepts used in traditional two step methods.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.159-178
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• 2001

In this paper we introduce a new concept of positive orthant dependence of multivariate stochastic processes. This concept is weaker than the POD but it enjoys most of the properties and preservation results of the POD. Some examples are presented.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1105-1116
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• 1996

A partial ordering is developed among weakly positive quadrant dependent (WPQD) bivariate random vectors. This permits us to measure the degree of WPQD-ness and to compare pairs of WPQD random vectors. Some properties and closures under certain statistical operations are derived. An application is made to measures of dependence such as Kendall's $\tau$ and Spearman's $\rho$.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.289-300
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• 2008

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.443-453
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• 2007

We study the equation of a membrane with strong viscosity. Based on the variational formulation corresponding to the suitable function space setting, we have proved the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.