Jun Haeng Heo

Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions

An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution functions corresponding to all observations. To overcome this drawback, the modified Anderson–Darling test was suggested by Ahmad et al. (1988b). In this study, the critical values of the modified Anderson–Darling test statistics are revised using simulation experiments with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance of the modified Anderson–Darling test. The results of the power study show that the modified Anderson–Darling test is more powerful than traditional tests such as the χ2, Kolmogorov–Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the modified Anderson–Darling test is applied to the annual maximum rainfall data in Korea.

Improving accuracy of IDF curves using long- and short-duration separation and multi-objective genetic algorithm

Multi-objective genetic algorithm (MOGA) and cumulative distribution function (CDF) are used to improve the accuracy of IDF curve. Rainfall durations are divided into short- and long-duration using root mean squared error (RMSE) and relative root mean squared error (RRMSE) between rainfall quantiles by IDF curve and at-site frequency analysis. RMSE could be used for estimating parameters of relatively long-duration, and RRMSE for short-duration. The compromised solutions could be ahieved through MOGA with two multi-objective functions. The duration separating technique called COMBI_1 is suggested and the comparison with the five different parameter estimation methods provides COMBI_1 is superior to the other methods.

Derivation of the Probability Plot Correlation Coefficient Test Statistics for the Generalized Logistic and the Generalized Pareto Distributions

The selection of appropriate probability distribution is important in frequency analysis to estimate the accurate quantile. Generally, the selection of appropriate probability model is based on the goodness of fit test. The probability plot correlation coefficient (PPCC) test has been known as powerful and easy test among the goodness of fit tests. In this study, the derivation of the PPCC test statistics for the generalized logistic distribution and the generalized Pareto distribution was performed by considering sample sizes, significance levels, and shape parameters. In addition, the correlation coefficients between orderly generated data sets and fitted quantiles were computed by using various plotting position formulas. Monte Carlo simulation was performed to select an appropriate plotting position formula for assumed probability distributions. As the results, the Gringorten’s plotting position formula was selected for given distributions. Finally, the PPCC test statistics for given probability distributions were derived from correlation coefficient values based on the selected plotting position formula considering various shape parameters.

Comparison of the Probability Plot Correlation Coefficient Test Statistics for the General Extreme Value Distribution

A proper probability distribution for estimating a quantile is selected by the goodness of fit tests in frequency analysis. The probability plot correlation coefficient(PPCC) test has been known as powerful and easy test among the goodness of fit tests. Generally, the PPCC test statistics are affected by significance levels, sample sizes, plotting position formulas, and shape parameters in case that a given distribution includes a shape parameter. Therefore, it is important to select an exact plotting position formula for the PPCC test statistics for a given probability distribution. After Cunnane(1978) defined the plotting position that related with the mean of data, many researches have accomplished about the plotting position formulas considered the influence of coefficients of skewness related with shape parameters. In this study, the PPCC test statistics are derived by using a plotting position formula developed from theoretical reduced variates with a term of a coefficient of skewness for the general extreme value(GEV) distribution. In addition, the PPCC test statistics are estimated by considering various sample sizes, significance levels, and shape parameters of the GEV distribution. The performance of derived PPCC test statistics is evaluated by estimating the rejection rate of population from Monte Carlo simulation.

Inflow forecasting for real-time reservoir operation using artificial neural network

Artificial neural network (ANN) is used for inflow forecasting of reservoir up to the next 12 hours. Numerical weather forecasting information (RDAPS), recorded rainfall data, water level of upstream dam and stream gauge site, and inflow of the current time are employed as input layer’s training values, and target value is +3, +6, +9, and +12 hours later inflow to Hwacheon reservoir in South Korea. Comparison result between ANN with RDAPS and without RDAPS shows that RDAPS information is useful for forecasting inflow of reservoir.

Selection of Variables for Regional Frequency Analysis of Annual Maximum Precipitation Using Multivariate Techniques

The regional frequency analysis is useful to estimate more accurate precipitation quantiles than the at-site frequency analysis, especially in case of regions with short record length like South Korea. In this study, the regionalization of annual maximum precipitation in South Korea was considered. The identification of homogeneous regions has a significant effect on quantile estimation in the regional frequency analysis. Various variables related to precipitation can be used to form regions. Since the type and number of variables may lead to improve the efficiency of partitioning, it is important to select those precipitation related variables, which represent most of the information from all candidate variables. Multivariate analysis techniques such as principal component analysis, factor analysis, and Procrustes analysis were used for this purpose. Finally, 33 variables were selected from the 42 candidate variables using multivariate techniques. A big loss of information due to dimension reduction was not found. Therefore, dimension reduction can promote the efficiency of cluster analysis. The selected variables can be successfully used to form regions for regional frequency analysis of annual maximum precipitation in South Korea.

Performance Evaluation of four Statistical Tests for Trend and Non-stationarity and Assessment of Observed and Projected Annual Maximum Precipitation Series in Major United States Cities

In this study, the performance of four statistical tests was evaluated to assess the following time-series types: stationary in variance and trend in mean (S_T), stationary in variance and no trend in mean (S_NT), nonstationary in variance and trend in mean (NS_T), and nonstationary in variance and no trend in mean (NS_NT). The four statistical tests included two stationarity tests, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Philips and Perron (PP) tests, and two trend tests, the Mann-Kendall (M-K) and regression tests. In each case, the sample size, standard deviation for noise, and several parameters were randomly generated to produce 1000 samples. The four tests were then conducted to determine if the data were stationary or non-stationary with trend or without trend. The results showed that there are several important patterns depending on the conditions of Monte Carlo experiments to investigate the performances of the four statistical tests with the four time-series types. These tests were also conducted to evaluate the time-series types of the observed and projected annual daily maximum precipitation series in eight cities of the United States. Results showed that cases of S_NT, which is the general assumption for the classical statistical frequency analysis, became less represented, while the two trend cases (NS_T and S_T) became more represented as time went on from HIST (1950–1999) to a representative concentration pathway (RCP) 4.5 or RCP 8.5 (2000–2099). NS_T cases in RCP 8.5 occurred more frequently than those in RCP 4.5. These results suggest that because of climate change, the assessment of time-series types should be considered when examining annual maximum precipitation and designing water-related infrastructure.

Derivation of the Modified Anderson-Darling Test Statistics for the Generalized Extreme Value and Generalized Logistic Distributions

An important problem in water resources engineering is the estimation of the flood magnitude for a certain return period. In flood frequency analysis, an assumed probability distribution is fitted to the available sample data to estimate the flood magnitude at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness-of-fit tests. However, previous goodness-of-fit tests give equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling test statistics which can give different weights to given data are provided using simulation. And the regression equations for the modified AndersonDarling test statistics are derived as a function of sample sizes and significance levels for the generalized extreme value and generalized logistic distributions.

ASYMPTOTIC VARIANCE OF REGIONAL GROWTH CURVE FOR GENERALIZED LOGISTIC DISTRIBUTION

The index flood method was introduced by Dalrymple to overcome the difficulties to obtain reliable estimates of the quantiles from relatively short record length. However, the application of index flood method must account for the additional uncertainty due to estimation of index flood at site. One must account for the uncertainties of the quantile estimates and those associated with the index flood. In this study, the generalized logistic distribution is considered as a an appropriate model for regional frequency analysis in Korea based on the method of probability weighted moments under the assumption that the regional quantiles and the index flood at site are independent. An approximate formulation of the variance of the quantile is introduced to evaluate the uncertainty of the estimated growth curve.