• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.85-95
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• 2012

In this paper we define extended negative quadrant dependence which is weaker negative quadrant dependence and show conditions for having extended negative quadrant dependence property. We also derive generalized Farlie-Gumbel-Morgenstern uniform distributions that possess the extended quadrant dependence property.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.795-805
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• 2011

In this paper, we study a family of continuous bivariate distributions that possesses the negative quadrant dependence property and the generalized negatively quadrant dependent F-G-M copula. We also develop the partial ordering of this new parametric family of negative quadrant dependent distributions.

• 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.

• Journal of TMJ Balancing Medicine
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• v.2 no.1
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• pp.13-16
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• 2012

Objectives: The quadrant theorem is a theorem proposed by C. M. Guzay in the field of functional, holistic dentistry. There are not much of scientific literature on the quadrant theorem. This study briefly reviewed basic concepts of quadrant theorem. Methods: A publication by Guzay and research articles were searched and reviewed. The quadrant theorem is depicted as a series of illustrations and accompanied explanations. Results: The primary concept of the quadrant theorem was presented in 1952. Based on geometric biophysics of the occlusion and related anatomical functions, physiological pivotal axis of the mandible is analyzed to occurs at the dens (the sub-atlas area). Composite muscular activity links the mandibular posture with C1-C2, which is then linked with the spinal posture. Twenty illustrations are progressively presented on the physiognomy, occlusion, and analysis of anatomical functions. The balanced distribution of the forces gives the durability of the functions in life. Conclusions: The quadrant theorem provides a functional linkage between the mandibular posture and the upper cervical vertebrae.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.767-775
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• 2014

In this paper we define the extended conditional negative quadrant dependence and generalize the conditional Borel-Cantelli lemma of B.L.S. Prakasa Rao(2012) to the case of pairwise extended conditionally negative quadrant dependence.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.163-171
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• 2013

By extending the negatively quadrant dependence, the paper puts forth the concept of extended negative quadrant dependence. A generalization of the second Borel-Cantelli lemma is obtained under extended negative quadrant dependence. Some applications are also introduced.

• Honam Mathematical Journal
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• v.28 no.2
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• pp.279-290
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• 2006

In this paper, we introduced a new notion of conditionally weakly positive quadrant dependence(CWPQD) between two random variables and the partial ordering of CWPQD is developed to compare pairs of CWPQD random vectors. Some properties and closure under certain statistical operations are derived.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.689-699
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• 2010

We discuss in this paper the notions of extended negative quadrant dependence and its properties. We study a class of bivariate uniform distributions having extended negative quadrant dependence, which is derived by generalizing the uniform representation of a well-known Farlie-Gumbel-Morgenstern distribution. Finally, we also study the limit behavior on the extended negative quadrant dependence.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.151-158
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• 1998

In this note we derive inequalities of linearly positive quadrant dependent random variables and obtain a strong law of large numbers for linealy positive quardant dependent random variables. Our results imply an extension of Birkel's strong law of large numbers for associated random variables to the linear positive quadrant dependence case.

• Proceedings of the Korean Information Science Society Conference
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• 2008.06a
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• pp.35-36
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• 2008