• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.271-288
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• 2003

In this paper, when the variance of the normal distribution is related to the mean, we develop noninformative priors such as matching priors and reference priors. We prove that the second order matching prior matches alternative coverage probabilities up to the same order and also it is a HPD matching prior. It turns out that one-at-a-time reference prior satisfies a second order matching criterion. Then using these noninformative priors, we develop a Bayesian test procedure for the equality of the means and variances of two independent normal distributions using fractional Bayes factor. Some simulation study is performed, and a real data example is also provided.

• Journal of the Korean Home Economics Association
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• v.28 no.1
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• pp.67-87
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• 1990

This study was designed with the purpose to analyze the bias and the factor structure of Need of Living and to clear the influence of related variables on Need on Living. The Degree of Importance(Di) and of sufficiency(Ds) of 65 indicators which were the constituent components of Need of Living and were extracted from the 51 preceeding studies was estimated by the 1084 samples including 614 urban and 470 rural residents through the questionaire. The indicators with higher Di and lower Ds than average were considered to show the high level of Need of Living. The main results are as follows; 1. Generally speaking, the level of Di was higher than that of Ds. Specially this was serious in the case of the indicators related with social-economic equity, employment, housing and environment. 2. Di level of the indicators such as physical health, judicial equality, the life of planned expenditure was highest. Specially the equity of income allocation was considered to be more important than the increase of income or asset itself. 3. Ds level of the indicators such as the life of plannel expenditure, the development of transportation and communication and the relationship between parents and children was highest, adn that of the use of leisure time, socialactivity, economic equality and social welfare was lowest. 4. Through the oblique rotation of Factor analysis, 12 factors were extracted (total eigen value 32.663, total variance 50.251%). Specially Factor 1 which was christened as the equality and development of social-economic life was related with 11 indicators and its common variance was 51.68%. 5. The rural residents, the lower income group and the lower educated group, who were told of being under disadvantage and unfair treatment of social-economic status, showed higher suffiency on the equity of income allocation, the freedom of living and expression, and judicial equality. 6. Generally speaking, the urban residents, the group under 39 years old, the higher educated group had more intensive Need of Living than the other groups.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.885-897
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• 2000

The use of an unweighted mean and of separate tests is part of the current practice for analyzing interlaboratory studies, and we hope to improve on this method. We fit, using maximum likelihood(ML), a rather intricate, multi-parameter measurement model with the material's true value as a latent variable in a situation where quite serviceable regression and ANOVA calculations have already been developed. The model fit leads to both a weighted estimate of he overall mean, and to tests for equality of means, slopes and variances. Maximum likelihood tests for difference among variances poses a challenge in that the likelihood can easily becoem unbounded. Thus the major objective become to provide a useful test of variance equality.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• The Korean Journal of Applied Statistics
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• v.35 no.5
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• pp.579-591
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• 2022

Functional data is collected in various fields. It is often necessary to test whether there are differences among groups of functional data. In this case, it is not appropriate to explain using the point-wise ANOVA method, and we should present not the point-wise result but the integrated result. Various studies on functional data analysis of variance have been proposed, and recently implemented those methods in the package fdANOVA of R. In this paper, I first explain ANOVA and multivariate ANOVA, then I will introduce various methods of analysis of variance for univariate and multivariate functional data recently proposed. I also describe how to use the R package fdANOVA. This package is used to test equality of weekly temperatures in Seoul and Busan through univariate functional data ANOVA, and to test equality of multivariate functional data corresponding to handwritten images using multivariate function data ANOVA.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.6
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• pp.9-16
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• 2020

This study aims to assess the effects of specimen thickness (ST) on fatigue crack growth in the early stages of crack propagation and near failure in magnesium alloys. The analysis of variance (ANOVA) method was adopted because fatigue crack propagation in magnesium alloys exhibits statistical behavior. The equality of variance test and residual diagnostics were performed on the grown cracks to confirm the validity of ANOVA by verifying the normal distribution and mutual independence of the residuals and their homoscedasticity. ANOVA confirmed that ST heavily impacts crack growth; i.e., when ST is smaller, cracks grow faster in the early crack propagation stage and break more quickly before the formation of larger cracks. We found that ST significantly affects fatigue crack growth in the early crack propagation stage and near the failure stage in magnesium alloys. The regression model was also used to predict crack formation near the failure stage.

• Interdisciplinary Bio Central
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• v.2 no.2
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• pp.4.1-4.6
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• 2010

The most common type of microarray experiment has a simple design using microarray data obtained from two different groups or conditions. A typical method to identify differentially expressed genes (DEGs) between two conditions is the conventional Student's t-test. The t-test is based on the simple estimation of the population variance for a gene using the sample variance of its expression levels. Although empirical Bayes approach improves on the t-statistic by not giving a high rank to genes only because they have a small sample variance, the basic assumption for this is same as the ordinary t-test which is the equality of variances across experimental groups. The t-test and empirical Bayes approach suffer from low statistical power because of the assumption of normal and unimodal distributions for the microarray data analysis. We propose a method to address these problems that is robust to outliers or skewed data, while maintaining the advantages of the classical t-test or modified t-statistics. The resulting data transformation to fit the normality assumption increases the statistical power for identifying DEGs using these statistics.

• Journal of Electrical Engineering and Technology
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• v.8 no.1
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• pp.80-89
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• 2013

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using a 'Mean-Variance Optimization (MVO)' algorithm with Kuhn-Tucker condition and swap process. The aim of the ED problem, one of the most important activities in power system operation and planning, is to determine the optimal combination of power outputs of all generating units so as to meet the required load demand at minimum operating cost while satisfying system equality and inequality constraints. This paper applies Kuhn-Tucker condition and swap process to a MVO algorithm to improve a global minimum searching capability. The proposed MVO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones, transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. The results are compared with those of the state-of-the-art methods as well.

• International Journal of Contents
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• v.3 no.1
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.9
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• pp.892-902
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• 2009

An efficient sequential optimization approach for metamodel was presented by Choi et al. This paper describes a new approach of the multilevel optimization method studied in Refs. [2] and [20,21]. The basic idea is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. After fitting a metamodel based on an initial space filling design, this model is sequentially refined by the expected improvement criterion. The advantages of the method are that it does not require optimum sensitivities, nonlinear equality constraints are not needed, and the method is relatively easy to understand and use. As a check on effectiveness, the proposed method is applied to an engineering example.