• KSCE Journal of Civil and Environmental Engineering Research
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• v.36 no.5
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• pp.791-803
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• 2016

Recently, frequency of extreme rainfall events in South Korea has been substantially increased due to the enhanced climate variability. Korea is prone to flooding due to being surrounded by mountains, along with high rainfall intensity during a short period. In the past three decades, an increase in the frequency of heavy rainfall events has been observed due to enhanced climate variability and climate change. This study aimed to analyze extreme rainfalls informed by their frequency of occurrences using a long-term rainfall data. In this respect, we developed a Poisson-Generalized Pareto Distribution (Poisson-GPD) based rainfall frequency method which allows us to simultaneously explore changes in the amount and exceedance probability of the extreme rainfall events defined by different thresholds. Additionally, this study utilized a Bayesian approach to better estimate both parameters and their uncertainties. We also investigated the synoptic patterns associated with the extreme events considered in this study. The results showed that the Poisson-GPD based design rainfalls were rather larger than those of based on the Gumbel distribution. It seems that the Poisson-GPD model offers a more reasonable explanation in the context of flood safety issue, by explicitly considering the changes in the frequency. Also, this study confirmed that low and high pressure system in the East China Sea and the central North Pacific, respectively, plays crucial roles in the development of the extreme rainfall in South Korea.

• 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.

• 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.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.835-844
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• 2010

Tools for statistical analysis of extreme values include the classical annual maximum method, the modern threshold method and variants improving the second one. While the annual maximum method is to t th generalized extreme value distribution to the annual maxima of a time series, the threshold method is to the generalized Pareto distribution to the excesses over a high threshold from the series. In this paper we deal with the Poisson-GPD method, a variant of the threshold method with a further assumption that the total number of exceedances follows the Poisson distribution, and apply it to the daily percentage increases and decreases computed from the spot prices of West Texas Intermediate, which were collected from January 4th, 1988 until December 31st, 2009. According to this analysis, the distribution of daily percentage increases as well as decreases turns out to have a heavy tail, unlike the normal distribution, which coincides well with the general phenomenon appearing in the analysis of lots of nowaday nancial data.

• 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.