• Communications for Statistical Applications and Methods
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• 제16권5호
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• pp.803-812
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• 2009

금융자료에 극단값이론을 적용하는 것은 위험관리에서 중요한 최신 통계기법 중의 하나라고 할 수 있다. 극단값분석에서 전통적으로 사용해 오던 연간 최대값방법은 시계열자료의 연간 최대값들에 대하여 일반화 극단값분포를 적합시키는 것이고, 최근 대안으로 널리 사용되고 있는 분계점 방법은 시계열자료 중 충분히 큰 하나의 분계점을 넘어서는 초과값들에 대하여 일반화파레토분포를 적합시키는 것이다. 그러나, 보다 실질적인 방법은 분계점을 넘어서는 초과값들을 하나의 점과정으로 해석하는 것인데, 즉 초과값들의 초과시점과 초과여분을 점근적으로 비동질 포아송과정을 갖는 하나의 2차원 점과정으로 간주하는 것이다. 본 논문에서는 이러한 2차원 비동질 포아송과정 모형을 1982.1.4부터 2008.12.31까지 수집된 원/달러 환율 시계열자료로부터 계산된 일별 환율투자손실률, 즉 일별 로그 손실률에 적용한다. 여기서 주된 관심은 10년 혹은 50년에 한번 정도 발생하는 대형 손실률 수준과 같은 극단분위수를 어떻게 추정하느냐 하는 것이다.

• Communications for Statistical Applications and Methods
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• 제26권3호
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• 대한수학회지
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• 제33권3호
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Journal of the Korean Data and Information Science Society
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• 제6권2호
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• pp.77-83
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• 1995

The inferences on a series system under the usual condition using data from constant stress partially accelerated life tests and type I censoring is studied. Two optimal designs to determine the sample proportion allocated each stress level model are also presented, which minimize the sum of the generalized asymptotic variances of maximum likelihood estimators of the failure rate and the acceleration factors and the sum of the asymptotic variances of maximum likelihood estimators of the acceleration factors for each component. Each component of a system is assumed to follow an exponenial distribution.

• Structural Engineering and Mechanics
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• 제29권5호
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• pp.551-565
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• 2008

Transient solution of asymmetric mechanical and thermal stresses for hollow cylinders made of functionally graded material is presented. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series.

• The Journal of Asian Finance, Economics and Business
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• 제8권11호
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• pp.31-39
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• 2021

This study empirically examines the proposition that the domestic fundamentals of a nation can emerge as absorptive capacity factors to reap the benefits of inward FDI. The study is contextualized in Asia, set from1982 to 2017, and data is grouped into low-income and lower-middle-income economies, in comparison to high-income and upper-middle-income economies, catering to different geographical regions within Asia. The investigation is based on a series of absorptive capacity factors such as infrastructure, human capital, domestic credit, and health indicator. The methodological analysis is premised on dynamic panel structure and employs the Generalized Method of Moments (GMM) estimation technique. The empirical findings suggest that that the infrastructure variable appears to be the major absorptive capacity factor for both groups of countries. The health indicator, on the other hand, can help reap the benefits of inward FDI, but only if the threshold level is met. The selected economies must achieve this threshold level to reap the benefits of FDI. To absorb the benefits of inward FDI, countries must be proactive in providing sound infrastructure and implementing proper healthcare measures.

• 한국수자원학회논문집
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• 제41권5호
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• pp.527-544
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• 2008

GPD 모형은 수문학 극치확률량 해석에 주로 적용되어 왔다. 극치 통계의 주목적은 드문 사상의 예측이며, 주요 문제점으로는 임계값 또는 임계값 초과치들에 대한 정확한 산정방법이 없어 그 추정이 매우 어렵다는 것이다. 본 연구에서는 임계값 또는 임계값 초과치들을 산정하기 위하여 4가지 방법을 적용하였다. 그 비교를 위하여 GPD 모형에 적용하여 7개의 지속시간(1, 2, 3, 6, 12, 18 및 24시간)과 10개의 재현기간(2, 3, 5, 10, 20, 30, 50, 70, 80 및 100년)에 대한 매개변수 및 Quantile을 추정하였다. 3변수 GPD의 매개변수 및 Quantile을 추정하기 위하여 MOM, ML과 PWM을 적용하였다. 적합도를 추정하기 위하여 K-S, CVM 및 A-D 검정을 수행하였고 Monte Carlo 실험으로 상대 제곱근오차를 산정하였다. 이러한 방법들을 이용하여 임계값 산정방법들을 비교하여 최적화된 방법을 추정하였다.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2016년도 학술발표회
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Communications for Statistical Applications and Methods
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• 제16권1호
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• pp.127-135
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• 2009

한국의 경제규모가 꾸준히 커감에 따라 가정, 건물, 공장 등에서 필요로 하는 전력량이 지속적으로 증가하고 있다. 전력공급의 안정화를 위해서는 최대전력량보다 전력공급능력이 높아야 한다. 월별 최대전력량을 잘 설명할 수 있는 통계모형을 찾기 위해 Winters 모형, 분해 시계열모형, ARMA 모형, 설명 변수를 통해 추세성분과 계절성분을 교정한 모형을 살펴보았다. 모형의 예측력 비교 기준으로 모형적합으로부터 구한 RMSE와 MAPE가 사용되었다. 여름철 최대전력량을 예측하기 위해 평균기온과 열대야 일수를 설명 변수로 갖는 시계열 모형이 가장 우수하였다. 아울러 외부요인을 갖는 극단분포 모형을 이용한 분석을 시도하였다.

• 한국농공학회:학술대회논문집
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• 한국농공학회 1998년도 학술발표회 발표논문집
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• pp.318-324
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• 1998

This study was conducted to derive optimal design floods by Generalized Extreme-value(GEV) distribution for the annual maximum series at ten watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was established by the tests of Independence, Homogeneity, detection of Outliers. L-coefficient of variation, L-skewness and L-kurtosis were calculated by L-moment ratio respectively. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in GEV distribution were compared by the relative mean and relative absolute error. It was found that design floods derived by the method of L-moments using weibull plotting position formula in GEV distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions in view of relative mean and relative absolute error.