• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.483-496
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• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.5-12
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• 2000

Meta-analysis refers to quantitative methods for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution and it is shown to be useful in such Bayesian meta-analysis. A general class of skewed elliptical distribution is reviewed and developed. These rich class of models combine the information of independent studies, allowing investigation of variability both between and within studies, and weight function. Here we investigate sensitivity of results to unobserved studies by considering a hierarchical selection model and use Markov chain Monte Carlo methods to develop inference for the parameters of interest.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.189-212
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• 2003

I review the current status of understanding when, how long, and how giant elliptical galaxies formed, focusing on the globular clusters. Several observational evidences show that massive elliptical galaxies formed at z > 2 (> 10 Gyr ago). Giant elliptical galaxies show mostly a bimodal color distribution of globular clusters, indicating a factor of $\approx$ 20 metallicity difference between the two peaks. The red globular clusters (RGCs) are closely related with the stellar halo in color and spatial distribution, while the blue globular clusters (BGCs) are not. The ratio of the number of the RGCs and that of the BGCs varies depending on galaxies. It is concluded that the BGCs might have formed 12-13 Gyr ago, while the RGCs and giant elliptical galaxies might have formed similarly 10-11 Gyr ago. It remains now to explain the existence of a gap between the RGC formation epoch and the BGC formation epoch, and the rapid metallicity increase during the gap (${\Delta}t{\approx}$ 2 Gyr). If hierarchical merging can form a significant number of giant elliptical galaxies > 10 Gyr ago, several observational constraints from stars and globular clusters in elliptical galaxies can be explained.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.25 no.6
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• pp.467-473
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• 2012

A functionally graded material (FGM) spacer, which the distribution of dielectric permittivity inside an insulator changes spatially, can considerably reduce the electric field concentration around a high-voltage electrode and along the gas-insulator interface when compared to a conventional spacer with a uniform permittivity distribution. In this research, we propose the FGM spacer with an elliptical permittivity distribution instead of that with a distribution of dielectric permittivity varying along a radial direction only in order to improve efficiently the insulation capability. The optimal design of the elliptical FGM spacer configuration is performed by using the response surface methodology (RSM) combined with the steepest descent method (SDM).

• Transactions of Materials Processing
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• v.9 no.5
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• pp.469-477
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• 2000

Most of researches have been performed on the formability of axisymmetric shape, but it is insufficient that the study on Process variables of elliptical deep drawing Product. There are many Process variables exerted influence on the formability of products. Particularly, blank shape is more important than the others in elliptical deep drawing process. In this study, blanks of three types were proposed and compared using thickness distribution and movement of sheet during the process. The aim of a paper is to obtain optimal blank shape through experiment and finite element analysis(FEA).

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.146-150
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• 2000

there are a lot of process variable exerted influence on the formability of products in deep drawing process. Particularly it is important that blank shape of the process variables. A paper to be connected with process variables of elliptical deep drawing products is insufficient the actual circumstances enough though researches have been performed on the deep drawing of sheet metal forming. In this study The effects of thickness distribution and movement of sheet are grasped as alteration of blank shapes in the process of elliptical deep drawing product and then optimal blank shape was presented. They were verified by the finite element analysis (FEA) and experiment.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under a non-normal distribution.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.373-391
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• 2022

The distribution of observations in most econometric studies with spatial heterogeneity is skewed. Usually, a single transformation of the data is used to approximate normality and to model the transformed data with a normal assumption. This assumption is however not always appropriate due to the fact that panel data often exhibit non-normal characteristics. In this work, the normality assumption is relaxed in spatial mixed models, allowing for spatial heterogeneity. An inference procedure based on Bayesian mixed modeling is carried out with a multivariate skew-elliptical distribution, which includes the skew-t, skew-normal, student-t, and normal distributions as special cases. The methodology is illustrated through a simulation study and according to the empirical literature, we fit our models to non-life insurance consumption observed between 1998 and 2002 across a spatial panel of 103 Italian provinces in order to determine its determinants. Analyzing the posterior distribution of some parameters and comparing various model comparison criteria indicate the proposed model to be superior to conventional ones.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.385-388
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• 2000

During the deep drawing process an initially flat blank is clamped between the die and the blank holder after which the punch moves down to deform the clamped blank into the desired shape. In general, sheet metal forming may involve stretching, drawing, bending or various combinations of those basic modes of deformation. The deformation problems of sheet metal working involve non-linearity in geometry and material. In this work, The punch load and thickness strain of electro-galvanized sheet steel (SECD) for elliptical deep drawing are examined under the various process conditions including, punch shape radius, die shape radius. The changes of punch load and thickness strain distribution of the deformed elliptical cup are affected by the size of each die shape radius.