• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.187-187
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• 1992

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.35-47
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• 2004

In this paper, we generalizes Kim and Bickel(2003)'s statistic for bivariate normality to that of multinormality, applying Fattorini(1986)'s method. Fattorini(1986) generalized Shapiro-Wilk's statistic for univariate normality to multivariate cases. The proposed statistic could be considered as an approximate statistic to Fattorini(1986)'s. It can be used even for a big sample size. Power performance of the proposed test is assessed in a Monte Carlo study.

• Journal of Korea Water Resources Association
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• v.45 no.8
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• pp.827-837
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• 2012

The estimation of the rainfall quantile is of great importance in designing hydrologic structures. Conventionally, the rainfall quantile is estimated by univariate frequency analysis with an appropriate probability distribution. There is a limitation in which duration of rainfall is restrictive. To overcome this limitation, bivariate frequency analysis by using 3 copula models is performed in this study. Annual maximum rainfall events in 5 stations are used for frequency analysis and rainfall depth and duration are used as random variables. Gumbel (GUM), generalized logistic (GLO) distributions are applied for rainfall depth and generalized extreme value (GEV), GUM, GLO distributions are applied for rainfall duration. Copula models used in this study are Frank, Joe, and Gumbel-Hougaard models. Maximum pseudo-likelihood estimation method is used to estimate the parameter of copula, and the method of probability weighted moments is used to estimate the parameters of marginal distributions. Rainfall quantile from this procedure is compared with various marginal distributions and copula models. As a result, in change of marginal distribution, distribution of duration does not significantly affect on rainfall quantile. There are slight differences depending on the distribution of rainfall depth. In the case which the marginal distribution of rainfall depth is GUM, there is more significantly increasing along the return period than GLO. Comparing with rainfall quantiles from each copula model, Joe and Gumbel-Hougaard models show similar trend while Frank model shows rapidly increasing trend with increment of return period.

• Journal of Korea Water Resources Association
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• v.42 no.9
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• pp.725-736
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• 2009

A flood event can be defined by three characteristics; peak discharge, total flood volume, and flood duration, which are correlated each other. However, a conventional flood frequency analysis for the hydrological plan, design, and operation has focused on evaluating only the amount of peak discharge. The interpretation of this univariate flood frequency analysis has a limitation in describing the complex probability behavior of flood events. This study proposed a bivariate flood frequency analysis using a Gumbel mixed model for the flood evaluation. A time series of annual flood events was extracted from observations of inflow to the Soyang River Dam and the Daechung Dam, respectively. The joint probability distribution and return period were derived from the relationship between the amount of peak discharge and the total volume of flood runoff. The applicability of the Gumbel mixed model was tested by comparing the return periods acquired from the proposed bivariate analysis and the conventional univariate analysis.

• Journal of Korea Water Resources Association
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• v.52 no.12
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• pp.985-999
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• 2019

Over the last decade, droughts have become more severe and frequent in many regions, and several studies have been conducted to explore the recent drought. Copula-based bivariate drought frequency analysis has been widely used to evaluate drought risk in the context of point frequency analysis. However, the relatively significant uncertainties in the parameters are problematic when available data are limited. For this reason, the primary purpose of this study is to develop a regional drought frequency model based on the Copula function. All parameters, including marginal and copula functions in the regional frequency model, were estimated simultaneously. Here, we present a case study of recent drought 2013-2015 over the Han-River watershed where severe drought risk is consistently found to increase. The proposed model provided a reliable way to significantly reduce the uncertainty of parameters with a Bayesian modeling framework. The uncertainty of the joint return period in the regional frequency analysis is nearly three times lower than that of the point frequency analysis. Accordingly, DIC values in the regional frequency analysis model are significantly decreased by 15. The results confirm that the proposed model is not only reliably representing characteristics of historical droughts and dependencies between drought variables, but also providing the efficacy of understanding regional drought characteristics.

• Journal of Korea Water Resources Association
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• v.47 no.2
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• pp.171-182
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• 2014

The objective of this study is to evaluate the utilization of bivariate joint drought index in South Korea. In order to develop the bivariate joint drought index, in this study, Clayton copula was used to estimate the joint distribution function and the calibration method was employed for parameter estimation. Precipitation and soil moisture data were selected as input data of bivariate joint drought index for period of 1977~2012. The time series analysis, ROC (Receiver Operating Characteristic) analysis, spatial analysis were used to evaluate the bivariate joint drought index with SPI (Standardized Precipitation Index) and SSI (Standardized Soil moisture Index). As a result, SPI performed better for drought onset and SSI for drought demise. On the other hand the bivariate joint drought index captured both drought onset and demise very well. The ROC score of bivariate joint drought index was higher than that of SPI and SSI, and it also reflected the local drought situations. The bivariate joint drought index overcomes the limitations of existing drought indices and is useful for drought analysis.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.1
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• pp.1-5
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• 2011

We furnished some properties of fuzzy testing of independence for correlation in a bivariate normal distribution by agreement index. First we present some restriction of the fuzzy data, define fuzzy sample correlation coefficient and agreement index for testing hypothesis with acceptance or rejection degree. Also, we show that UMP unbiased fuzzy test and drawing conclusions the fuzzy test.

• Journal of Korea Water Resources Association
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• v.45 no.2
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• pp.191-201
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• 2012

This study reviewed the parameter estimation procedure of the Freund bivariate exponential distribution for the decision of the annual maximum rainfall event. The method of moments was reviewed first, whose results were compared with those from the method of maximum likelihood. Both methods were applied to the hourly rainfall data of the Seoul rain gauge station measured from 1961 to 2010 to select the annual maximum rainfall events, which were also compared each other. The results derived are as follows. First, when applying the method of moments for the parameter estimation, it was found necessary to consider the correlation coefficient between the two variables as well as the mean and variance. Second, the method of maximum likelihood was better to reproduce the mean, but the method of moments was better to reproduce the annual variation of the variance. Third, The annual maximum rainfall events derived were very similar in both cases. Among differently selected annual maximum rainfall events, those with the higher rainfall amount were selected by the method of maximum likelihood, but those with the higher rainfall intensity by the method of moments.

• Journal of Korea Water Resources Association
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• v.45 no.7
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• pp.713-727
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• 2012

In this study, the bivariate frequency analysis of the independent annual rainfall event series was done to be used for the runoff analysis, whose results were also compared with those from the conventional univariate frequency analysis. This study was applied to three differently-sized basins such as the Joongryang Stream, Chunggye Stream, and Ooyi Stream. The Clark model was used as the runoff model, and the SCS method was applied for the calculation of the effective rainfall. The alternating block method and the Huff method were considered to be compared for the temporal distribution of rainfall event. Summarizing the results are as follows. (1) The difference between the univariate and bivariate frequency analysis results were large when the rainfall duration was short, but significantly decreased as the rainfall duration increased. The univariate frequency analysis results were bigger when the rainfall duration was short, but smaller in opposite case. (2) The peak flow derived by applying the alternating block method was bigger than that by the Huff method. Also, the peak flow when applying the alternating block method increased as the rainfall duration increased, but converged smoothly around the rainfall duration of 24 hours. (3) For the Joongryang Stream, when applying the Huff method, the peak flow derived for the bivariate frequency analysis was bigger than that for the univariate case, but for the other two basins, the results were opposite. When applying the alternating block method, the results were consistent for all three basins that the peak flow derived by applying the bivariate frequency analysis was bigger than those by the univariate frequency analysis.

• The Korean Journal of Applied Statistics
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• v.12 no.2
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• pp.553-561
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• 1999

이변량 정규분포의 상관계수 $\rho$에 대한 검정 및 신뢰구간을 구하는 모수적 방법으로서 Fisher의 z 변환과 해당하는 점근적 분포가 널리 쓰이고 있다. 본 연구에서는 이에 대한 대안으로서 직교변환과 F 분포를 활용하는 방법을 제시한다. 후자의 방법이 전자와 비교하여 사실상 대등하면서도 설명은 오히려 쉬우므로 통계학 교육에 더 적합하다고 생각한다. 또한, 시험적으로, $H_0$:$\rho$=$\rho_0$에 대한 모수적 임의화 검정법을 제안한다.