• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.435-442
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• 1993

For the generalized gamma distribution, exact inferences about quantiles need many computations involving complicated numerical integrations. This paper suggests approximate confidence intervals which are easily obtained by considering the alternative location-scale model. Also, these intervals are very accurate even for small sample size. Approximate confidence intervals about quantiles in the lognormal distribution are also considered. With type 2 censoring data, approximate confidence intervals can also be obtained directly by the suggested methods.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.255-268
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• 2020

A mixture of multivariate canonical fundamental skew t-distribution (CFUST) has been of interest in various fields. In particular, interest in the unsupervised learning society is noteworthy. However, fitting the model via EM algorithm suffers from significant processing time. The main cause is due to the calculation of many multivariate t-cdfs (cumulative distribution functions) in E-step. In this article, we provide an approximate, but fast calculation method for the in univariate fashion, which is the product of successively conditional univariate t-cdfs with Taylor's first order approximation. By replacing all multivariate t-cdfs in E-step with the proposed approximate versions, we obtain the admissible results of fitting the model, where it gives 85% reduction time for the 5 dimensional skewness case of the Australian Institution Sport data set. For this approach, discussions about rough properties, advantages and limits are also presented.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.189-207
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• 2021

In this paper, we consider the approximate controllability for a class of semilinear integro-differential functional control equations in which nonlinear terms of given equations satisfy quasi-homogeneous properties. The main method used is to make use of the surjective theorems that is similar to Fredholm alternative in the nonlinear case under restrictive assumptions. The sufficient conditions for the approximate controllability is obtain which is different from previous results on the system operator, controller and nonlinear terms. Finally, a simple example to which our main result can be applied is given.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2004.08a
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• pp.264-268
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• 2004

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.793-804
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• 2009

The hypotheses of difference, ratio and odds ratio between two proportions are used for the non-inferiority trial. The approximate unconditional test suggested by Kang and Chen (2000) based on difference and ratio have the potential problem against the failure rate. When the sample size is small, the type I errors of the asymptotic test using the normal approximation suggested by Chen et al. (2000) tends to exceed the nominal level. Therefore, we propose the approximate unconditional test based on odds ratio and compare the test with the asymptotic test. And we compare the three hypotheses used in the approximate unconditional tests of two proportions with respect to the type I errors and power.

• The Journal of the Korea Contents Association
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• v.14 no.10
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• pp.1-9
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• 2014

Generally, integral image used for autostereoscopic 3d display is generated for flat lens array, but flat lens array cannot provide a wide range of view for generated integral image because of narrow range of view. To make up for this flat lens array's weak point, curved lens array has been proposed, and due to technical and cost problem, approximate surface lens array composed of several flat lens array is used instead of ideal curved lens array. In this paper, we constructed an approximate surface lens array arranged for $20{\times}8$ square flat lens in 100mm radius sphere, and we could get about twice angle of view compared to flat lens array. Specially, unlike existing researches which manually generate integral image, we propose an OpenCL GPU parallel process algorithm for generating real-time integral image. As a result, we could get 12-20 frame/sec speed about various 3D volume data from $15{\times}15$ approximate surface lens array.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.181-192
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• 2016

We consider several methods to approximate option prices with correction terms to the Black-Scholes option price. These methods are able to compute option prices from various risk-neutral distributions using relatively small data and simple computation. In this paper, we compare the performance of Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method of using Normal inverse gaussian distribution, and an asymptotic method of using nonlinear regression through simulation experiments and real KOSPI200 option data. We assume the variance gamma model in the simulation experiment, which has a closed-form solution for the option price among the pure jump $L{\acute{e}}vy$ processes. As a result, we found that methods to approximate an option price directly from the approximate price formula are better than methods to approximate option prices through the approximate risk-neutral density function. The method to approximate option prices by nonlinear regression showed relatively better performance among those compared.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.339-348
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• 2001

More often a commercial package for the structural analysis is necessary in the structural optimum design. In this case the task of combining the package with an optimization program must be required, hut it is not so simple because interchanging some data between them is difficult. Sequential approximate optimization is currently used as a natural way to overcome the hard task. If sequential approximate optimization has wide side constraints that the lower limit of design variables is very small and their upper limit is very large, it is not so easy to obtain approximated functions accurately for the whole design domain. This paper proposes a sequential design domain method, which is very useful to carry out sequential approximate optimization in this case. In this paper, the response surface methodology is used to obtain approximated functions and the orthogonal array is used for design of experiments. The sequential approximate optimization of 3-bar and 10-bar trusses is demonstrated to verify the reliability of the sequential design domain method.