• 충청수학회지
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• 제21권1호
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• pp.99-106
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• 2008

In this paper, we establish some recurrence relations which is satisfied by the quotient moments of the lower record values from the standard generalized extreme value (GEV) distribution.

• Communications for Statistical Applications and Methods
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• 제15권5호
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• pp.793-798
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• 2008

Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.817-826
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• 2007

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the location parameter in a generalized extreme value distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• 한국해양공학회지
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• 제33권3호
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• pp.222-228
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• 2019

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.463-477
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• 2009

극단치 분포의 모수 추정방법으로 최우추정법, 확률가중적률법, 회귀분석법은 기존 연구에서 활발하게 적용되어져 왔다. 그러나 이들 세 가지 추정방법 가운데, 회귀분석법의 우수성은 엄격하게 평가되어진 적이 없다. 본 논문에서는 몬테칼로 시뮬레이션을 통하여 Generalized Extreme Value(GEV) 분포와 Generalized Pareto(GP) 분포의 모수 추정에 회귀분석법 및 다른 추정방법을 적용하여 비교 연구한다. 시뮬레이션 결과, 표본의 크기가 작은 경우 회귀분석 법은 GEV 분포의 위치모수 추정시 편의 측면과 효율성 측면에서 다른 방법보다 우수한 경향을 나타내었다. GP 분포의 규모모수 추정시에는 표본의 크기 가 작을 경우 회귀분석법이 다른 방법보다 작은 편의를 나타내었다. 회귀분석법은 표본의 크기 가 작거나 적당히 큰 경우에도 GEV 분포나 GP 분포의 형태모수 추정시에 형태모수의 값이 -0.4일 경우, 다른 방법보다 우수한 경향을 나타내었다.

• 응용통계연구
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• 제27권6호
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• pp.947-958
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• 2014

집중호우의 특성을 이해하는 것은 수문관리 및 재해방재 등에서 매우 중요하다. 특히 반환주기는 이러한 집중호우의 특성을 나타내는 측정치로 자주 사용된다. 본 논문에서는 베이지안 계층적 모형을 이용하여 강우의 반환주기에 대한 공간구조를 분석하였다. 먼저 국내 62개 지점에서 측정한 강우 강도을 기초로 하여 연간 일일 최대강우량과 특정한 수준을 초과하는 강우량에 대해서 generalized extreme value(GEV)와 generalized Pareto distribution(GPD)를 각각 가정하여 추정하였다. 집중호우 반환주기에 대한 공간구조는 이 GEV 분포와 GPD 분포의 모수에 공간구조를 가지는 다변량 정규분포를 이용하여 설명하였다. 제안된 모형을 국내 76개 지역에서 39년간 측정된 일별 강우량 관측자료에 적용하였다.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.523-529
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• 2010

In this paper, we obtain some recurrence relations for the quotient moments of the lower record values from the generalized extereme value(GEV) distribution. We also deduce some recurrence relations for the negative moments from the GEV distribution.

• Wind and Structures
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• 제34권6호
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• pp.469-482
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• 2022

The generalized extreme value distribution (GEVD) is frequently used to fit the block maximum of environmental parameters such as the annual maximum wind speed. There are several methods for estimating the parameters of the GEV distribution, including the least-squares method (LSM). However, the application of the LSM with the expected order statistics has not been reported. This study fills this gap by proposing a fitting method based on the expected order statistics. The study also proposes a plotting position to approximate the expected order statistics; the proposed plotting position depends on the distribution shape parameter. The use of this approximation for distribution fitting is carried out. Simulation analysis results indicate that the developed fitting procedure based on the expected order statistics or its approximation for GEVD is effective for estimating the distribution parameters and quantiles. The values of the probability plotting correlation coefficient that may be used to test the distributional hypothesis are calculated and presented. The developed fitting method is applied to extreme thunderstorm and non-thunderstorm winds for several major cities in Canada. Also, the implication of using the GEVD and Gumbel distribution to model the extreme wind speed on the structural reliability is presented and elaborated.

• 대한수학회보
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• 제45권1호
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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.

• Journal of the Korean Data and Information Science Society
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• 제24권4호
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• pp.857-865
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• 2013

집중 호우로 인한 피해가 증가하면서 다양한 기법들을 이용하여 강우량 예측에 대한 관심이 높아졌다. 최근에는 극단분포를 활용하여 강우량을 예측하려는 시도가 늘고 있다. 본 연구에서는 일반화 극단 분포를 활용하여 실제 서울시의 1973년부터 2010년까지 7월달의 사후예측분포를 생성하고, 수치적인 계산을 위해서 MCMC (Markov chain Monte Carlo)알고리즘을 활용하였다. 이 연구를 통해서 사후예측분포의 점추정값들을 비교하였고 2011년 7월달의 자료와 비교해 봤을 때 집중 호우의 확률이 증가한 것을 알 수 있었다.