• Water for future
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• v.7 no.2
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• pp.107-111
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• 1974

Annual runoff in the Nakdong river basin has been analyzed to find the probability functions of best fit to distribution of historical annual runoff. The results obtained are as follows; (1) Log-normal 3-parameter disrtibution is believed as the probability function of best fit to historical distribution (2) Log-normal 3-parameter disrtibution is believed as the best fit probability function among Log-normal dist-ributions. (3) In the test of goodness of fit, $x^2-test$ shows that probability of $x^2-valus$ in Log-normal 3-parameter distribution is nearly more than 90%. But in the Simirnov-Kolmogorov test, hypotheses for the probability distributions cannot be rejected at significance level 5% & 1%. (4) Among 7 gauging stations, Dongchon & Koryung-Bridge's records show lower fitness to the theoretical probability functions than other 5 gauging station's

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.607-617
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• 2012

The goodness-of-fit test for multivariate normal distribution is important because most multivariate statistical methods are based on the assumption of multivariate normality. We propose goodness-of-fit test statistics for multivariate normality based on the modified squared distance. The empirical percentage points of the null distribution of the proposed statistics are presented via numerical simulations. We compare performance of several test statistics through a Monte Carlo simulation.

• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.3
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• pp.253-258
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• 2015

The purpose of this study is to find suitable probability distribution function of complex distribution data like multimodal. Normal distribution is broadly used to assume probability distribution function. However, complex distribution data like multimodal are very hard to be estimated by using normal distribution function only, and there might be errors when other distribution functions including normal distribution function are used. In this study, we experimented to find fit probability distribution function in multimodal area, by using AIS(Automatic Identification System) observation data gathered in Mokpo port for a year of 2013. By using chi-squared statistic, gaussian mixture model(GMM) is the fittest model rather than other distribution functions, such as extreme value, generalized extreme value, logistic, and normal distribution. GMM was found to the fit model regard to multimodal data of maritime traffic flow distribution. Probability density function for collision probability and traffic flow distribution will be calculated much precisely in the future.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2353-2360
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• 2000

Statistical fatigue properties of metallic materials are increasingly required for reliability design purpose. In this study, static and fatigue tests were conducted and the normal, log-normal, two -parameter Weibull distributions at the 5% significance level are compared using the Kolmogorov-Smirnov goodness-of-fit test. Parameter estimation were compared with experimental results using the maximum likelihood method and least square method. It is found that two-parameter Weibull distribution and maximum likelihood method provide a good fit for static and fatigue life data. Therefore, it is applicable to the static and fatigue life analysis of the spheroidal graphite cast iron. The P-S-N curves were evaluated using log-normal distribution, which showed fatigue life behavior very well.

• Water for future
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• v.7 no.2
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• pp.99-106
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• 1974

The records of wave heights which were observed at Muk ho and Po hang of the East Coast of Korea were analized by several probility functions. The exponential 2 parameter distribution was found as the best fit probability function to the historical distribution of wave heights by the test of goodness of fit. But log-normal 2 parameter and log-extremal type A distributions were also fit to the historical distribution, especially in the Smirnov-Kolmogorov test. Therefore, it can't be always regarded that those two distributions are not fit to the wave heiht's distribution. In the test of goodness of fit, the Chi-Square test gave very sensitive results and Smirnov-Kolmogorov test, which is a distribution free and non-parametric test, gave more inclusive results. At the next stage, the inter-relationship between the mean and the one-third wave heights, the mean and the one-=tenth wave heights, the one-third and the one-tenth wave heights, the one-third and the highest wave heights were obtained and discussed.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• Structural Engineering and Mechanics
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• v.28 no.3
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• pp.263-280
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• 2008

Information on the distribution of the basic random variable is essential for the accurate analysis of structural reliability. The usual method for determining the distributions is to fit a candidate distribution to the histogram of available statistical data of the variable and perform approximate goodness-of-fit tests. Generally, such candidate distribution would have parameters that may be evaluated from the statistical moments of the statistical data. In the present paper, a cubic normal distribution, whose parameters are determined using the first four moments of available sample data, is investigated. A parameter table based on the first four moments, which simplifies parameter estimation, is given. The simplicity, generality, flexibility and advantages of this distribution in statistical data analysis and its significance in structural reliability evaluation are discussed. Numerical examples are presented to demonstrate these advantages.

• Wind and Structures
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• v.31 no.4
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• pp.299-309
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• 2020

In this study, wind data such as speeds, loads and potential of Muğla which is located in the southwest of Turkey were statistically analyzed. The wind data which consists of hourly wind speed between 2010 and 2013 years, was measured at the 10-meters height in four different ground stations (Datça, Fethiye, Marmaris, Köyceğiz). These stations are operated by The Turkish State Meteorological Service (T.S.M.S). Furthermore, wind data was analyzed by using Log-Normal and Gamma distributions, since these distributions fit better than Weibull, Normal, Exponential and Logistic distributions. Root Mean Squared Error (RMSE) and the coefficients of the goodness of fit (R²) were also determined by using statistical analysis. According to the results, extreme wind speed in the research area was 33 m/s at the Datça station. The effective wind load at this speed is 0.68 kN/㎡. The highest mean power densities for Datça, Fethiye, Marmaris and Köyceğiz were found to be 46.2, 1.6, 6.5 and 2.2 W/㎡, respectively. Also, although Log-normal distribution exhibited a good performance i.e., lower AD (Anderson - Darling statistic (AD) values) values, Gamma distribution was found more suitable in the estimation of wind speed and power of the region.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.60-74
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• 2002

In this study, normal, log-normal, triangular, uniform. Weibull, Erlang and unit beta probability density functions are tried to represent the behaviour of frequency distributions of workpiece dimensions collected from various manufacturing firms. Among the distribution functions, the unit beta distribution function is found to be the best fit using the chi-square test of fit. An attempt is made for the adoption of the unit beta model to x-bar charts of quality control in manufacturing. In this direction, upper and lower control limits (UCL and LCL) of x-bar control charts of dimension measurements are estimated for the beta model, and the observed differences between the beta and normal model control limits are discussed for the measurement sets.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.