• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.423-430
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• 2004

We provide the exact form of a Rao-Robson version of the chi-squared test of multivariate normality suggested by Park(2001). This test is easy to apply in practice since it is easily computed and has a limiting chi-squared distribution under multivariate normality. A self-contained formal argument is provided that it has the limiting chi-squared distribution. A simulation study is provided to study the accuracy, in finite samples, of the limiting distribution. Finally, a simulation study in a nonnormal distribution is conducted in order to compare the power of our test with those of other popular normality tests.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.91-103
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• 2006

Yun (2005) introduced an estimator of the second order parameter characterizing the tail behavior of probability distributions and proved its consistency. In this paper we prove its asymptotic normality under a third order condition.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.85-94
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• 2011

The aim of this paper is to study the normality of fuzzy topological spaces in Kubiak-$\check{S}$ostak's sense. Also, some characterizations and the effects of some types of functions on these types of normality are studied.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.83-89
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• 1997

In this paper we generalize the concept of normality for the problem involving set functions in a view of Jahn. The main result is that the problem with Slater's constraint qualification is normal and stable.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.415-421
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• 2002

Because most common assumption is normality in statistical analysis, testing normality is very important. We propose a new plot and test statistic to test for normality based on the modified Lorenz curve that is proved to be a powerful tool to measure the income inequality within a population of income receivers. We also compare the proposed test statistics with the W test (Shapiro and Wilk (1965)), TL test (Kang and Cho (1999)) in terms of the power of test through by Monte Carlo method. The proposed test is more usually powerful than the other tests except some case.

• Journal of the Korea Safety Management & Science
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• v.10 no.3
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• pp.237-243
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• 2008

The present study proposes two normality tests using nonparametric rank measures for small sample such as modified normal probability paper(NPP) tests and modified Ryan-Joiner Test. This research also reviews various normality tests such as $X^2$ test, and Kullback-Leibler test. The proposed normality tests can be efficiently applied to the sparsity tests of factor effect or contrast using saturated design in $k^n$ factorial and fractional factorial design.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.119-129
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• 2003

We propose a new logistic regression model of normality curves for normal(diseased) and abnormal(nondiseased) classifications by neural networks in data mining. The fitted logistic regression lines are estimated, interpreted and plotted by the neural network technique. A few goodness-of-fit test statistics for normality are discussed and the performances by the fitted logistic regression lines are conducted.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.247-257
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• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• 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.