• Journal of the Korean Society of Hazard Mitigation
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• v.9 no.3
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• pp.127-133
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• 2009

In this study, dimensionless-cumulative rainfall curves were generated by multivariate Monte Carlo method. For generation of rainfall curve rainfall storms were divided and made into dimensionless type since it was required to remove the spatial and temporal variances as well as differences in rainfall data. The dimensionless rainfall curves were divided into 4 types, and log-ratio method was introduced to overcome the limitations that elements of dimensionless-cumulative rainfall curve should always be more than zero and the sum total should be one. Orthogonal transformation by Johnson system and the constrained non-normal multivariate Monte Carlo simulation were introduced to analyse the rainfall characteristics. The generative technique in stochastic rainfall variation using multivariate Monte Carlo method will contribute to the design and evaluation of hydrosystems and can use the establishment of the flood disaster prevention system.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.411-423
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• 2003

In this paper we develop a method for calculating a probability that a particular generalized variance is the smallest of all the K multivariate normal generalized variances. The method gives a way of comparing K multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approach for the probability is intractable and thus a Bayesian method is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach. Necessary theory involved in the method and computation is provided.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.65-85
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• 2024

The tail probability of a function of a multivariate random variable is not easy to estimate by the crude Monte Carlo simulation. When the occurrence of the function value over a threshold is rare, the accurate estimation of the corresponding probability requires a huge number of samples. When the explicit form of the cumulative distribution function of each component of the variable is known, the inverse transform likelihood ratio method is directly applicable scheme to estimate the tail probability efficiently. The method is a type of the importance sampling and its efficiency depends on the selection of the importance sampling distribution. When the cumulative distribution of the multivariate random variable is represented by a copula and its marginal distributions, we develop an iterative algorithm to find the optimal importance sampling distribution, and show the convergence of the algorithm. The performance of the proposed scheme is compared with the crude Monte Carlo simulation numerically.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.53-67
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• 1996

Numerous classical as well as robust methods have been proposed in the literature for the detection of multiple outlier in multivariate data. The effectiveness and power of each of these methods have not been thoroughly investigated. In this paper we first reduce the vast number of outlier detection methods to a small number of viable ones. This reduction is based on previous work of other researches and on some theoretical arguments. Then we design and implement a Monte Carlo experiment for comparing these methods. The main goal of our study is to determine which methods are most powerful in the detection of multiple outlier and in dealing with the masking and swamping problems. The results of the Monte Carlo study indicate that two of the methods seem to hace better performances than the others for the detection of multiple outlier in multivariate data.

• Korean Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.215-221
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• 1997

A new approach in solving design centering problem is presented. Like most stochastic optimization problems, optimal design centering problems have intrinsic difficulties in multivariate intergration of probability density functions. In order to avoid to avoid those difficulties, genetic algorithm and very coarse Monte Carlo simulation are used in this research. The new algorithm performs robustly while producing improved yields. This result implies that the combination of robust optimization methods and approximated simulation schemes would give promising ways for many stochastic optimizations which are inappropriate for mathematical programming.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.225-232
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• 2000

The linear and quadratic discrimination functions based on normal theory are widely used to classify an observation to one of predefined groups. But the discriminant functions are sensitive to outliers. A high breakdown procedure to estimate location and scatter of multivariate data is the minimum volume ellipsoid or MVE estimator To obtain high breakdown classifiers outliers in multivariate data are detected by using the robust Mahalanobis distance based on MVE estimators and the weighted estimators are inserted in the functions for classification. A samll-sample MOnte Carlo study shows that the high breakdown robust procedures perform better than the classical classifiers.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.443-455
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• 1999

A simulation-based approach to estimating the probability of an arbitrary region under a multivariate normal distribution is developed. In specific, the probability is expressed as the ratio of the unrestricted and the restricted multivariate normal density functions, where the restriction is given by the region whose probability is of interest. The density function of the restricted distribution is then estimated by using a sample generated from the Gibbs sampling algorithm.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.765-777
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• 2003

In this paper, we investigate some measures as tests of multivariate normality based on principal components. The idea was proposed by Srivastava and Hui(1987). They generalized Shapiro-Wilk statistic for multi variate cases. We show the null distributions of the statistics do not depend on the unknown parameters and mention the asymptotic null distributions. Also power performance of the tests are assessed in a Monte Carlo study.