• Honam Mathematical Journal
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• v.42 no.3
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• pp.577-590
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• 2020

In this paper, new subclasses of analytic functions are proposed by using Mittag-Leffler function. Also some properties of these classes are studied in regard to coefficient inequality, distortion theorems, extreme points, radii of starlikeness and convexity and obtained numerous sharp results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.6
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• pp.480-494
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• 2009

Long term extreme wave data are essential for planning and designing coastal structures. Since the availability of the field data for the waters around Korean peninsula is limited to provide a reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. KORDI(2005) has proposed extreme wave data at 106 stations off the Korean coast from 1979 to 2003. In this paper, extreme data sets of wave(KORDI, 2005) have been analyzed for best-fitting distribution functions, for which the spread parameter proposed by Goda(2004) is evaluated. The calculated values of the spread parameter are in good agreement with the values based on method of moment for parameter estimation. However, the spread parameter of extreme wave data has a representative value ranging from about 1.0 to 2.8 which is larger than some foreign coastal waters, it is necessary to review deep water design wave.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.803-812
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• 2009

The application of extreme value theory to financial data is a fairly recent innovation. The classical annual maximum method is to fit the generalized extreme value distribution to the annual maxima of a data series. An alterative modern method, the so-called threshold method, is to fit the generalized Pareto distribution to the excesses over a high threshold from the data series. A more substantial variant is to take the point-process viewpoint of high-level exceedances. That is, the exceedance times and excess values of a high threshold are viewed as a two-dimensional point process whose limiting form is a non-homogeneous Poisson process. In this paper, we apply the two-dimensional non-homogeneous Poisson process model to daily losses, daily negative log-returns, in the data series of KBW/USD exchange rate, collected from January 4th, 1982 until December 31 st, 2008. The main question is how to estimate extreme quantiles of losses such as the 10-year or 50-year return level.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1001-1012
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• 2016

It is well known that air pollutants exert a bad influence on human health. According to the United Nations Environment Program, 4.3 million people die from carbon monoxide and particulate matter annually from all over the world. Carbon monoxide is a toxic gas that is the most dangerous of the gas consisting of carbon and oxygen. In this paper, we used 1 hour, 6 hours, 12 hours, and 24 hours average carbon monoxide concentration data collected between 2004 and 2013 in Daegu Gyeongbuk area. Parameters of the generalized extreme value distribution were estimated by maximum likelihood estimation and L-moments estimation. An evalution of goodness of fitness also was performed. Since the number of samples were small, L-moment estimation turned out to be suitable for parameter estimation. We also calculated 5 year, 10 year, 20 year, and 40 year return level.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.9
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• pp.1746-1752
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• 2002

Fatigue fracture in machine components is produced by surface micro-crack from stress concentration area such as notch and material defect. It is difficult to predict the remaining fatigue lift of mechanical components because the surface micro-crack on critical area initiates and grows with statistical distribution. Plane bending fatigue tests were carried out on the plain specimen of Al 2024-T3 and the initiation and growth behavior of surface micro cracks were observed. The statistical distribution of surface length of multiple micro cracks and their maximum length were investigated. The maximum surface crack length distributions were analyzed on the basis of the statistics of extremes in order to examine the prediction of remaining life.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.8
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• pp.2529-2551
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• 2022

Visual servoing (VS) based on the Kalman filter (KF) algorithm, as in the case of KF-based image-based visual servoing (IBVS) systems, suffers from three problems in uncalibrated environments: the perturbation noises of the robot system, error of noise statistics, and slow convergence. To solve these three problems, we use an IBVS based on KF, African vultures optimization algorithm enhanced extreme learning machine (AVOA-ELM), and fuzzy logic (FL) in this paper. Firstly, KF online estimation of the Jacobian matrix. We propose an AVOA-ELM error compensation model to compensate for the sub-optimal estimation of the KF to solve the problems of disturbance noises and noise statistics error. Next, an FL controller is designed for gain adaptation. This approach addresses the problem of the slow convergence of the IBVS system with the KF. Then, we propose a visual servoing scheme combining FL and KF-AVOA-ELM (FL-KF-AVOA-ELM). Finally, we verify the algorithm on the 6-DOF robotic manipulator PUMA 560. Compared with the existing methods, our algorithm can solve the three problems mentioned above without camera parameters, robot kinematics model, and target depth information. We also compared the proposed method with other KF-based IBVS methods under different disturbance noise environments. And the proposed method achieves the best results under the three evaluation metrics.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.287-302
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• 1998

Saddlepoint approximation to the distribution function of sample mean(Daniels, 1987) is extended to the case of general statistic in this paper. The suggested approximation methods are applied to derive the approximations to the distributions of some statistics, including sample valiance and studentized mean. Some comparisons with other methods show that the suggested approximations are very accurate for moderate or small sample sizes. Even in extreme tail the accuracies are also maintained.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.537-542
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• 2001

In recent engineering, the designer has become more and more dependent on computer simulation. But defining exact model using computer simulation is too expensive and time consuming in the complicate systems. Thus, designers often use approximation models, which express the relation between design variables and response variables. These models are called metamodel. In this paper, we introduce one of the metamodel, named Kriging. This model employs an interpolation scheme and is developed in the fields of spatial statistics and geostatistics. This class of interpolating model has flexibility to model response data with multiple local extreme. By reason of this multi modality, we can't use any gradient-based optimization algorithm to find global extreme value of this model. Thus we have to introduce global optimization algorithm. To do this, we introduce DE(Differential Evolution). DE algorithm is developed by Ken Price and Rainer Storn, and it has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. This algorithm is similar to GA(Genetic Algorithm) in populating points, crossing over, and mutating. But it introduces vector concept in populating process. So it is very simple and easy to use. Finally, we show how we determine Kriging metamodel and find global extreme value through two mathematical examples.

• Journal of the Society of Naval Architects of Korea
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• v.33 no.1
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• pp.145-152
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• 1996

In this study, the technique to evaluate the extreme design wave height of certain return period is developed from the given measured or hindcasted sea state data of concerned area for limited period. By using the order statistics and Monte Carlo Simulation method, the best fit probability distribution function with proper parameters describing the given wave height data is chosen, from which extreme design wave height can be predicted by extrapolation to the desired return period. The fitness and the confidence limit of the chosen probability function are also discussed. Application calculation is carried out for the wave height data given by applying the Wilson wave model theory to major 50 typhoon wind data affecting Korean South coast during the year from 1938 to 1987.

• The Journal of the Convergence on Culture Technology
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• v.8 no.1
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• pp.531-536
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• 2022

This paper compared the performance of the parametric method and the nonparametric method when estimating the distribution for the tail of the distribution with heavy tails. For the parametric method, the generalized extreme value distribution and the generalized Pareto distribution were used, and for the nonparametric method, the kernel density estimation method was applied. For comparison of the two approaches, the results of function estimation by applying the block maximum value model and the threshold excess model using daily fine dust public data for each observatory in Seoul from 2014 to 2018 are shown together. In addition, the area where high concentrations of fine dust will occur was predicted through the return level.