• Communications for Statistical Applications and Methods
• /
• v.15 no.6
• /
• pp.1013-1026
• /
• 2008

Kolmogorov-Smirnov(K-S) statistic has been widely used for the model validation of credit rating models. Validation criteria for the K-S statistic is empirically used at the levels of 0.3 or 0.4 which are much larger than the critical values of K-S test statistic. We examine whether these criteria are reasonable and appropriate through the simulations according to various sample sizes, type II error rates, and the ratio of bads among data. The simulation results say that the currently used validation criteria are too lower than values of K-S statistics obtained from any credit rating models in Korea, so that any credit rating models have good discriminatory power. In this work, alternative criteria of K-S statistic are proposed as critical levels under realistic situations of credit rating models.

• Communications for Statistical Applications and Methods
• /
• v.4 no.2
• /
• pp.435-444
• /
• 1997

The objective of this study is to investigate the problem of goodness of fit testing based on nonparametric function estimation techniques for the random censorship model. The small and large sample properties of the proposed test, $E_{mn}$, were investigated and it is shown that under the proportional hazard model $E_{mn}$ has higher power compared to the powers of the Kolmogorov -Smirnov, Kuiper, Cramer-von Mises, and analogue of the Cramer-von Mises type test statistic.

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.2
• /
• pp.261-272
• /
• 2009

Kolmogorov-Smirnov (K-S) statistic has been widely used for testing homogeneity of two distributions in the credit rating models. Joseph (2005) used K-S statistic to obtain validation criteria which is most well-known. There are other homogeneity test statistics such as the Cramer-von Mises, Anderson-Darling, and Watson statistics. In this paper, these statistics are introduced and applied to obtain criterion of these statistics by extending Joseph (2005)'s work. Another set of alternative criterion is suggested according to various sample sizes, type a error rates, and the ratios of bads and goods by using the simulated data under the similar situation as real credit rating data. We compare and explore among Joseph's criteria and two sets of the proposed criterion and discuss their applications.

• Journal of the Korean Data and Information Science Society
• /
• v.6 no.1
• /
• pp.31-37
• /
• 1995

We consider density estimates of the usual type generated by a kernel function. By using the limit theorems for the maximum of normalized deviation of the estimate from its expected value, we propose to use data dependent bandwidth in the tests of goodness of fit based on these statistics. Also a small sample Monte Carlo simulation is conducted and proposed method is compared with Kolmogorov-Smirnov test.

• Journal of the Korean Data and Information Science Society
• /
• v.27 no.5
• /
• pp.1399-1412
• /
• 2016

We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.

• Journal of Korean Society of Water and Wastewater
• /
• v.12 no.3
• /
• pp.99-106
• /
• 1998

This paper presents a procedure for determining the design rainfall depth and the design rainfall intensity at Incheon city area in Korea. In this study the eight probability distributions are considered to estimate the probable rainfall depths for 11 different durations. The Kolmogorov - Smirnov test and the Chi-square test are adopted to test each distribution. The probable rainfall intensity formulas are then determined by i) the least squares (LS) method, ii) the least median squares (LMS) method, iii) the reweighted least squares method based on the LMS (RLS), and iv) the constrained regression (CR) model. The Talbot, the Sherman, the Japanese, and the Unified type are considered to determine the best type for the Incheon station. The root mean squared (RMS) errors are computed to test the formulas derived by four methods. It is found that the Unified type is the most reliable and that all methods presented herein are acceptable for determining the coefficients of rainfall intensity formulas from an engineering point of view.

• Journal of Korea Water Resources Association
• /
• v.37 no.3
• /
• pp.173-184
• /
• 2004

The objective of this study is to examine the usefulness of climate model simulations (GCM) in Korea water resource management. The methods are based on probabilistic measures of the effectiveness of GCM simulations of an indicator variable for discriminating high versus low regional observations of a target variable. The formulation uses the significance probability of the Kolmogorov-Smirnov test for detecting differences between two variables. AMIP-II(Atmospheric Model Intercomparison Project-II) type GCM simulation done by ECMWF(European Centre for Medium-Range Weather Forecasts) was used for indicator variable and observed mean average precipitation(MAP) values on 7 major river basins were used as target variable. Monte Carlo simulation is used to establish the significance of the estimator values. The results show that GCM simulations done by ECMWF are skillful in discriminating the high from the low of the observed MAP for wet season in all seven basins of Korea, but not enough for dry season.

• Journal of Korean Society of Water and Wastewater
• /
• v.8 no.2
• /
• pp.35-42
• /
• 1994

This study is to analyse probability distribution characteristics of water supply demand. Two cities located near Seoul were selected as study areas. In this study, two probalility distribution types were tested using the K-S(Kolmogorov-Smirnov) method. The K-S method was used to prove the goodness of the selected distribution type. And also, the goodness of maximum day demand to average day demand ratio which was obtained by field data was tested. Conclusions are as follows. 1.Bothl normal distribution type and lognormal distribution type are appropriate as the probalility distribution type for the water supply demand. 2. The probability distribution characteristics can be used to test the goodness of the maximum day to average day demand ratio.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2004.05b
• /
• pp.595-598
• /
• 2004

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.41 no.6
• /
• pp.33-43
• /
• 1999

Drought is a serious diaster in agriculutre, especially to upland crops. Hence, the Agricultural Drought Analysis Model (ADAM) that is integratable with GIS was applied to analyae agriculture drought in upland. ADAM is composed of two sub-models , one is a Soil Water Balance Model (SWBM) and the other is a Drougth Analysis Model (DAM) that is based on the Runs theory. The ADAM needs weather data, rainfall data and soil physical characteristics data as input and calculates daily soil moisture contents. GIS was integrated to the ADAM for the calculation of regional soil moisture using digitized landuse map, detaile dsoil map, thiessen network and district boundary . For the agriculutral drought analysis, the ADAM adapt the Runs theory for analyzing drought duration, severity and magnitude . Log-Pearson Type-III probability distribution function and Kolmogorov-Smirnov test were used to test the fitness of good of the model. The integration of ADAM with GIS was successfully implemented and would be operated effectively for the regional drought analysis.