• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.471-485
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• 2010

VaR is used extensively as a tool for risk management by financial institutions. For convenience, the normal distribution is usually assumed for the measurement of VaR, but recently the method using extreme value theory is attracted for more accurate VaR estimation. So far, GEV and GPD models are used for probability models of EVT for the VaR estimation. In this paper, the PP model is suggested for improved VaR estimation as compared to the traditonal EV models such as GEV and GPD models. In view of the stochastic process, the PP model is regarded as a generalized model which include GEV and GPD models. In the empirical analysis, the PP model is shown to be superior to GEV and GPD models for the performance of VaR estimation.

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.109-122
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• 2018

The composite lognormal-generalized Pareto distribution (LN-GPD) is a mixture of right-truncated lognormal and GPD for a given threshold value. Scollnik (Scandinavian Actuarial Journal, 2007, 20-33, 2007) shows that the composite LN-GPD is adequate to describe body distribution and heavy-tailedness. This paper considers time-varying modeling of the LN-GPD based on local polynomial maximum likelihood estimation. Time-varying model provides significant detailed information of time dependent data, hence it can be applied to disciplines such as service engineering for staffing and resources management. Our work also extends to Beirlant and Goegebeur (Journal of Multivariate Analysis, 89, 97-118, 2004) in the sense of losing no data by including truncated lognormal distribution. Our proposed method is shown to perform adequately in simulation. Real data application to the service time of the Israel bank call center shows interesting findings on the staffing policy.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1053-1057
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• 2008

본 연구에서는 산악형 강수 해석을 위해 제주도내 강우관측 자료를 이용하여 확률강우량 산정 및 고도와의 선형회귀분석을 수행하였다. 제주도내 강우관측 자료는 기상관서 4개소 및 AWS(Automatic Weather System, 자동기상관측소) 13개소의 자료를 활용하였다. 확률강우량 산정시 AWS 강우관측 자료는 AMS(Annual Maximum Series, 연 최대치 계열) 모형을 적용하기에는 자료기간이 충분하지 않으므로 짧은 자료기간에 적합한 PDS(Partial Duration Series, 부분 기간치 계열) 모형을 적용하였다. 따라서 본 연구에서는 PDS의 대표적인 분포형인 GPD(Generalized Pareto Distribution)를 적용하여 지속시간별 확률강우량을 산정하였다. 산정된 지속시간별 확률강우량과 고도와의 관계를 확인하기 위하여 선형회귀분석을 수행하였다. 회귀분석 결과 확률강우량은 고도가 증가함에 따라 선형적으로 증가하였다. 또한, 재현기간이 길어질수록 고도에 따른 확률강우량 증가율도 증가하였다. 다만, 재현기간과 관계없이 지속시간이 짧을 경우 확률강우량과 고도와의 선형 관계는 약해지는 것으로 나타났다.

• Journal of Korea Water Resources Association
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• v.41 no.5
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• pp.527-544
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• 2008

Generalized Pareto distribution (GPD) is frequently applied in hydrologic extreme value analysis. The main objective of statistics of extremes is the prediction of rare events, and the primary problem has been the estimation of the threshold and the exceedances which were difficult without an accurate method of calculation. In this paper, to obtain the threshold or the exceedances, four methods were considered. For this comparison a GPD model was used to estimate parameters and quantiles for the seven durations (1, 2, 3, 6, 12, 18 and 24 hours) and the ten return periods (2, 3, 5, 10, 20, 30, 50, 70, 80 and 100 years). The parameters and quantiles of the three-parameter generalized Pareto distribution were estimated with three methods (MOM, ML and PWM). To estimate the degree of fit, three methods (K-S, CVM and A-D test) were performed and the relative root mean squared error (RRMSE) was calculated for a Monte Carlo generated sample. Then the performance of these methods were compared with the objective of identifying the best method from their number.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.453-453
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• 2017

본 연구에서는 최근 기후변화로 인한 집중호우의 발생횟수의 경향을 확률적으로 분석함에 있어 1개월 동안 80 mm/day 이상의 강우사상을 집중호우로 정의하여, 대구 및 부산 강우관측소로부터 수집된 384개월 동안의 집중호우를 분석하였다. 집중호우 월별 발생횟수와 같은 형식의 자료의 확률적 분석은 대개 Poisson 분포 (POI)가 사용되나 자료에 포함된 0자료의 과잉은 확률분포를 왜곡시키는 문제를 발생시킨다. 본 연구에서는 이 문제를 개선하기 위하여 개발된 일반화 Poisson 확률분포 (GPD), 0-과잉 Poisson 확률분포 (ZIP), 0-과잉 일반화 Poisson 확률분포 (ZIGP), Bayesian 0-과잉 일반화 Poisson 확률분포 (Bayesian ZIGP)를 집중호우 자료에 적용하고, 5개 모형의 특성을 비교분석하였으며, Bayesian ZIGP 모형의 구축에 있어서는 정보적 사전분포를 사용함으로써 모형의 정확도를 개선하였다. 분석결과 분석하고자 하는 자료에 0이 과다하게 포함되어 있는 경우 POI 및 GPD 분포는 관측결과와는 다른 결과를 제시하여 적절한 모형으로 고려되지 못함을 알 수 있었다. 5가지 모형 중 정보적 사전분포를 탑재한 Bayesian ZIGP 모형이 가장 관측 자료와 유사한 결과를 도출하였으나 모형의 구축에 수반되는 실용적인 측면을 고려하면 ZIP 모형도 충분히 사용될 수 있는 모형으로 추천되었다.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.947-958
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• 2014

Understanding extreme precipitation events is very important for flood planning purposes. Especially, the r-year return level is a common measure of extreme events. In this paper, we present a spatial analysis of precipitation return level using hierarchical Bayesian modeling. For intensity, we model annual maximum daily precipitations and daily precipitation above a high threshold at 62 stations in Korea with generalized extreme value(GEV) and generalized Pareto distribution(GPD), respectively. The spatial dependence among return levels is incorporated to the model through a latent Gaussian process of the GEV and GPD model parameters. We apply the proposed model to precipitation data collected at 62 stations in Korea from 1973 to 2011.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011

This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1479-1494
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• 2015

Since the Markowitz's mean-variance framework for portfolio analysis, the topic of portfolio optimization has been an important topic in finance. Traditional approaches focus on maximizing the expected return of the portfolio while minimizing its variance, assuming that risky asset returns are normally distributed. The normality assumption however has widely been criticized as actual stock price distributions exhibit much heavier tails as well as asymmetry. To this extent, in this paper we employ the genetic algorithm to find the optimal portfolio under the Value-at-Risk (VaR) constraint, where the tail of risky assets are modeled with the generalized Pareto distribution (GPD), the standard distribution for exceedances in extreme value theory. An empirical study using Korean stock prices shows that the performance of the proposed method is efficient and better than alternative methods.

• Journal of Korea Water Resources Association
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• v.49 no.6
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• pp.481-493
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• 2016

The statistical analysis to the torrential rainfall data that is defined as a rainfall amount more than 80 mm/day is performed with Daegu and Busan rainfall data which is collected during 384 months. The number of occurrence of the torrential rainfall events can be simulated usually using Poisson distribution. However, the Poisson distribution can be frequently failed to simulate the statistical characteristics of the observed value when the observed data is zero-inflated. Therefore, in this study, Generalized Poisson distribution (GPD), Zero-Inflated Poisson distribution (ZIP), Zero-Inflated Generalized Poisson distribution (ZIGP), and Bayesian ZIGP model were used to resolve the zero-inflated problem in the torrential rainfall data. Especially, in Bayesian ZIGP model, a informative prior distribution was used to increase the accuracy of that model. Finally, it was suggested that POI and GPD model should be discouraged to fit the frequency of the torrential rainfall data. Also, Bayesian ZIGP model using informative prior provided the most accurate results. Additionally, it was recommended that ZIP model could be alternative choice on the practical aspect since the Bayesian approach of this study was considerably complex.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.246-246
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• 2016

본 연구에서는 최근 기후변화로 인한 집중호우의 발생횟수의 경향을 확률적으로 분석함에 있어 1개월 동안 80 mm/day 이상의 강우사상을 집중호우로 정의하여, 대구 및 부산 강우관측소로부터 수집된 384개월 동안의 집중호우를 분석하였다. 집중호우 월별 발생횟수와 같은 형식의 자료의 확률적 분석은 대개 Poisson 분포 (POI)가 사용되나 자료에 포함된 0자료의 과잉은 확률분포를 왜곡시키는 문제를 발생시킨다. 본 연구에서는 이 문제를 개선하기 위하여 개발된 일반화 Poisson 확률분포 (GPD), 0-과잉 Poisson 확률분포 (ZIP), 0-과잉 일반화 Poisson 확률분포 (ZIGP), Bayesian 0-과잉 일반화 Poisson 확률분포 (Bayesian ZIGP)를 집중호우 자료에 적용하고, 5개 모형의 특성을 비교분석하였으며, Bayesian ZIGP 모형의 구축에 있어서는 정보적 사전분포를 사용함으로써 모형의 정확도를 개선하였다. 분석결과 분석하고자 하는 자료에 0이 과다하게 포함되어 있는 경우 POI 및 GPD 분포는 관측결과와는 다른 결과를 제시하여 적절한 모형으로 고려되지 못함을 알 수 있었다. 5가지 모형 중 정보적 사전분포를 탑재한 Bayesian ZIGP 모형이 가장 관측 자료와 유사한 결과를 도출하였으나 모형의 구축에 수반되는 실용적인 측면을 고려하면 ZIP 모형도 충분히 사용될 수 있는 모형으로 추천되었다.