• Proceedings of the KSME Conference
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• 2003.04a
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• pp.604-609
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• 2003

Flaw geometries, applied stress, and material properties are major input variables for the fracture mechanics analysis. Probabilistic approach can be applied for the consideration of uncertainties within these input variables. But probabilistic analysis requires many assumptions due to the lack of initial flaw distributions data. In this study correlations are examined between initial flaw distributions and in-service flaw distributions on structures under cyclic load. For the analysis, LEFM theories and Monte Carlo simulation are applied. Result shows that in-service flaw distributions are determined by initial flaw distributions rather than fatigue crack growth rate. So initial flaw distribution can be derived from in-service flaw distributions.

• Proceedings of the Korean Geotechical Society Conference
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• 2002.03a
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• pp.245-252
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• 2002

The Rock mass in which constructed a tunnel consist of the geological formations or the engineering rock type. Each layers are distinguished by the mineral, weathering and distributions of faults and Joints. Therefore, a tunneling design in rock mass starts from understanding and analyzing of the various geological engineering factors and then the engineering characteristics and distributions for each layers are determined to analysis and collection of the efficient informations. For this working, next two problems have to be solved. First, the layers in rock mass have to be classified and their distributions have to be defined. Second, the rock mass classifications and distributions based on the standard engineering classification have to be determined. Efficiently to approaching this two problems, the best solution is all geotechnical data are embodied to 3-D.

• The Korean Journal of Applied Statistics
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• v.27 no.1
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• pp.1-11
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• 2014

The Weighted Logrank test and its special case, Logrank test are widely used to compare survival distributions; however, these methods are inappropriate when the sample size is small or censoring distributions are not equal since they use test statistics from approximate distributions. A permutation test can be an alternative for small sample cases; however, this should be used only when censoring distributions are equal. To handle cases with small sample size and unequal censoring distributions, the permutation-imputation method was developed to compare two survival distributions. In this paper, approximate method, permutation method and permutation-imputation method were compared using a Logrank test and Prentice-Wilcoxon test for three or more survival distributions comparison.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• Journal of Food Hygiene and Safety
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• v.7 no.2
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• pp.113-121
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• 1992

Food intake data from 228 persons (96 male adult ranging in age from 19 to 54, 27 female adult ranging in age from 20 to 46, 54 boys ranging in age from 9 to 11, and 51 girls ranging in age from 8 to II) were studied with respect to the shape of the underlying probablity distributions. For each menu items distributional shapes of food intake were different. Most of distributions for food intakes from normaJ distributions. From food intake data of 2 meals nutrition intake data are calculated. For each meal, energy, protein, fat, carbohydrate, fiber, calcium, iron, vitamin A, thiamin, ribofavin, niacin and vitamin C were computed and thier distributions were compared with normal distributions. Distributions for adult female showed normal distributions for some food items. For nutrient intake data from male adults, distributions for vitamin C from 1st meal and calcium from 2nd meal were marginal and the remains were differed from normal distributions. For adult female and childern, distiributions for some nutients were differed from normal distributions. It is hard to find special patterns for each nutrient distributions. Therefore the normal distributions assumptions should be verified prior to applying parametric techniques to thier data. If those assumptions are not valid, non-parametric techniques should be used to analyze their data.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.45-51
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• 1993

For studies in reliability, biometry and survival analysis, the length biased distribution is frequently appropriate for certain natural sampling plans. So, we shall convey the preservation of some partial orderings under life length biasd distributions and closures of ILR and NBU classes under life length biasd distributions.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.247-255
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• 2003

Hypothesis testing for the equality of two distributions were considered. Nonparametric kernel density estimates were used for testing equality of distributions. Cross-validatory choice of bandwidth was used in the kernel density estimation. Sampling distribution of considered test statistic were developed by resampling method, called the bootstrap. Small sample Monte Carlo simulation were conducted. Empirical power of considered tests were compared for variety distributions.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.591-602
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• 2012

In present paper we establish conditions for the integrability of various distributions of GCR-lightlike submanifolds and obtain conditions for the distributions to define totally geodesic foliations in GCR-lightlike submanifolds.