• 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.

• 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.

• 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.