• Proceedings of the Korean Operations and Management Science Society Conference
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• 1999.04a
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• pp.46-46
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• 1999

• 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.26 no.6
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• pp.583-589
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• 2019

Counterexamples of a skew-normal distribution are developed to improve our understanding of this distribution. Two examples on bivariate non-skew-normal distribution owning marginal skew-normal distributions are first provided. Sum of dependent skew-normal and normal variables does not follow a skew-normal distribution. Continuous bivariate density with discontinuous marginal density also exists in skew-normal distribution. An example presents that the range of possible correlations for bivariate skew-normal distribution is constrained in a relatively small set. For unified skew-normal variables, an example about converging in law are discussed. Convergence in distribution is involved in two separate examples for skew-normal variables. The point estimation problem, which is not a counterexample, is provided because of its importance in understanding the skew-normal distribution. These materials are useful for undergraduate and/or graduate teaching courses.

• School Mathematics
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• v.12 no.3
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• pp.273-299
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• 2010

The purpose of the study is designing and implementing 'Sampling Distributions Simulation' to help students to understand concepts of sampling distributions. This computer simulation is developed to help students understand sampling distributions more easily. 'Sampling Distributions Simulation' consists of 4 sessions. 'The first session - Confidence level and confidence intervals - includes checking if the intended confidence level is actually achieved by the real relative frequency for the obtained sample confidence intervals containing population mean. This will give the students clearer idea about confidence level and confidence intervals in addition to the role of sampling distribution of the sample means among those. 'The second session - Sampling Distributions - helps understand sampling distribution of the sample means, through the simulation method to make comparison between the histogram of sampling distributions and that of the population. The third session - The Central Limit Theorem - includes calculating the means of the samples taken from a population which follows a uniform distribution or follows a Bernoulli distribution and then making the histograms of those means. This will provides comprehension of the central limit theorem, which mentions about the sampling distribution of the sample means when the sample size is very large. The forth session - the normal approximation to the binomial distribution - helps understand the normal approximation to the binomial distribution as an alternative version of central limit theorem. With the practical usage of the shareware 'Sampling Distributions Simulation', we expect students to have a new vision on the sampling distribution and to get more emphasis on it. With the sound understandings on the sampling distributions, more accurate and profound statistical inferences are expected. And the role of the sampling distribution in the inferences should be more deeply appreciated.

• Journal of Navigation and Port Research
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• v.34 no.8
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• pp.609-614
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• 2010

This paper describes statistical parameter estimation to calculate collision probabilities between Mokpo Harbor Bridge and passing vessels. At first, we obtained AIS (Automatic Identification System) information from passing vessels, then after, analyzed the lateral distributions of vessel tracks and estimated the mean and the standard deviation for the distance away from bridge center, the passing course and the passing speed. The analysis results of track distribution for the distance away and the passing course are shown as normal type, otherwise the speed distribution shown as two kinds of different normal type. In addition, we testified that the usefulness of estimated parameter values through the relative comparison between the track distributions and it's normal probability distributions.

• The Korean Journal of Financial Management
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• v.25 no.4
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• pp.79-116
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• 2008

This paper examines and estimates GARCH-VaR models (RiskMetrics, GARCH, IGARCH, GJR and APARCH) with three different distributions such as Gaussian normal, Student-t, Skewness Student-t Distribution using the daily price data from Korean Stock Market during Jan. 1, 1980-Sept. 30, 2004. It also compares them. In-sample test, this finds that for all confidence level as $90%{\sim}99.9%$, the performance and accuracy of IGARCH with ${\lambda}=0.87$ and skewness Student-t distribution are superior to other models and distributions in long position, but GARCH and GJR with Skewness Student-t distribution in short position. For above 99% confidence level, the performance and accuracy of IGARCH with ${\lambda}=0.87$ in both long and short positions are superior to other models and distributions, but Skewness Student-t distribution for long position and Student-t distribution for short position are more accuracy and superior to other distributions. In-out-of sample test, these results also confirm the evidences that the above findings are consistent as well.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2003.11a
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• pp.601-608
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• 2003

Thermal analyses have been carried out for a spent fuel dry storage cask under normal and off-normal conditions. Environmental temperature is assumed to be $15^{\circ}C$ under the normal condition. The off-normal condition has an environmental temperature of $38^{\circ}C$. An additional off-normal condition is considered as a partial blockage of the air inlet ducts. Two of the four air inlet ducts are assumed to be completely blocked. The maximum temperatures of the fuel rod and concrete overpack were lower than the allowable values under the normal condition. Temperature distributions for the off-normal conditions were slightly higher than the normal conditions.

• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.97-111
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• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

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

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 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.