• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.587-592
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• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Journal of the Korean Society of Safety
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• v.31 no.6
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• pp.25-31
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• 2016

This paper has analyzed the structure, applicable regulations and the resistance characteristics of insulation ring type of CSST (Corrugated Stainless Steel Tubing for Gas). With the flammability test conducted in accordance with KS C IEC 60811-1-1, the evaluation of insulation resistance, temperature characteristics, and reliability has been conducted. An insulation ring type CSST consists of protective coating, tube, nut, insulation ring, packing, socket, and ball valve. Connecting an insulation ring type CSST to gas tubings for gas appliance is not permitted, moreover, the product shall be installed inside a sleeve pipe in case of buried installation such as the ceiling. Damages on protective coating and tube were detected when fire was applied to the test sample with a portable torch for 60 seconds. The insulation resistance of a normal product was $49.59M{\Omega}$, while that of the product completed the flammability test reduced to $9.21M{\Omega}$. The mean insulation resistance within the confidence Interval of 95% using the mini tap program 17 was $49.59M{\Omega}$ and the mean insulation resistance within the confidence interval reduced to $9.21M{\Omega}$. In the normal distribution analysis of 95% confidence interval, the value-P of the normal product was stable at 0.075 and AD(Anderson-Darling) statistic value was turned out to be 0.063, which is very normal, and the standard deviation was analyzed as 0.2586. The value P of the product completed the flammability test resulted in 0.005, the AD was 1.355 and the standard deviation reduced to 0.07908.

• 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.

• Geomechanics and Engineering
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• v.35 no.5
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• pp.499-509
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• 2023

The objective of this study is to perform outlier analysis to obtain the distribution of groundwater levels through the best model. The groundwater levels are measured in 10, 25 and 30 piezometers in Seoul, Daejeon and Suncheon in South Korea. Fifty-eight empirical distribution functions were applied to determine a suitable fit for the measured groundwater levels. The best fitted models based on the measured values are determined as the Generalized Pareto distribution, the Johnson SB distribution and the Normal distribution for Seoul, Daejeon and Suncheon, respectively; the reliability is estimated through the Anderson-Darling method. In this study, to choose the appropriate confidence interval, the relationship between the amount of outlier data and the confidence level is demonstrated, and then the 95% is selected at a reasonable confidence level. The best model shows a smaller error ratio than the GEV while the Mahalanobis distance and outlier labelling methods results are compared and validated. The outlier labelling and Mahalanobis distance based on median shown higher validated error ratios compared to their mean equivalent suggesting, the methods sensitivity to data structure.