• 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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.75-93
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• 2008

The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.495-510
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• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.165-168
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• 2002

This paper describes the dynamics of the weak shock wave propagating inside some kinds of branched pipe bends. Computations are carried out by solving the two-dimensional, compressible, unsteady Euler Equations. The second-order TVD(Total Variation Diminishing) scheme is employed to discretize the governing equations. For computations, two types of branched pipe($90^{\circ}$ branch,$45^{\circ}$ branch) with a diameter of D are used. The incident normal shock wave is assumed at D upstream of the pipe bend entrance, and its Mach number is changed between 1.1 and 2.4. The flow fields are numerically visualized by using the pressure contours and computed schlieren images. The comparison with the experimental data performed for the purpose of validation of computational work. Reflection and diffraction of the propagating shock wave are clarified. The present computations predicted the experimented flow field with a good accuracy.

• Journal of computational fluids engineering
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• v.13 no.1
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• pp.57-62
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• 2008

Laminar flows over a cube and a cuboid (cube extended in the streamwise direction) are numerically investigated for the Reynolds numbers between 50 and 350. First, vortical structures behind a cube and lift characteristics are scrutinized in order to understand the variation in vortex shedding characteristics with respect to the Reynolds number. As the Reynolds number increases, the flow over a cube experiences the steady planar-symmetric, unsteady planar-symmetric, and unsteady asymmetric flows. Similar to the sphere wake, the planar-symmetric flow over a cube can be divided into two different regimes: single-frequency regime and multiple-frequency regime. The former has a single frequency due to regular shedding of vortices with the same strength in time, while the latter has multiple frequency components due to temporal variation in the strength of shed vortices. Second, the effect of the length-to-height ratio of the cuboid on the flow characteristics is investigated for the Reynolds number of 270, at which planar-symmetric vortex shedding takes place behind a cube. With the ratio smaller than one, the flow over the cuboid becomes unsteady asymmetric flow, whereas it becomes steady flow for the ratios greater than one. With increasing the ratio, the drag coefficient first decreases and then increases. This feature is related to the flow reattachment on the side faces of the cuboid.