• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.2
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• pp.193-198
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• 2011

By a nonnegative sign pattern we mean a matrix whose entries are from the set {+, 0}. A nonnegative sign pattern A is said to allow normality if there is a normal matrix B whose entries have signs indicated by A. In this paper we investigated some nonnegative normal pattern that is different to the pattern in [1]. Some interesting constructions of nonnegative integer normal matrices are provided.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.507-518
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• 2004

Malkovich & Afifi (1973) generalized the univariate skewness and kurtosis to test a hypothesis of multivariate normality by use of the union-intersection principle. However these statistics are hard to compute for high dimensions. We propose the approximate statistics to them, which are practical for a high dimensional data set. We also compare the proposed statistics to Mardia(1970)'s multivariate skewness and kurtosis by a Monte Carlo study.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.501-510
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• 2020

Mardia (Biometrika, 57, 519-530, 1970) defined measures of multivariate skewness and kurtosis. Based on these measures, omnibus test statistics of multivariate normality are proposed using normalizing transformations. The transformations we consider are normal approximation and a Wilson-Hilferty transformation. The normalizing transformation proposed by Enomoto et al. (Communications in Statistics-Simulation and Computation, 49, 684-698, 2019) for the Mardia's kurtosis is also considered. A comparison of power is conducted by a simulation study. As a result, sum of squares of the normal approximation to the Mardia's skewness and the Enomoto's normalizing transformation to the Mardia's kurtosis seems to have relatively good power over the alternatives that are considered.

• The Mathematical Education
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• v.41 no.1
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• pp.109-126
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• 2002

In this thesis. we estimated the good reliability coefficient ${\beta}$$\sub$k/ that is unbiased, consistent and more efficient than Cronbach's ${\alpha}$$\sub$k/ in splitting of a test into several formats of subtests and several properties of ${\beta}$$\sub$k/ are also represented. The tables of coefficients of skewness and kurtosis are represented to test the significance of departures from normality. We got the cumulative normal plots of z'from the distribution which is departed from normality using the Bock's approximation procedure and we finally enumerated the transformed standardized scores z'and a new raw score X' which enable us to proceed further evaluation procedures depending on our assessment policy.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.337-347
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• 1995

In the problem of some sequential estimation, the stopping times may be written in the form $N(c) = inf{n \geq n_0; n \geq c^2 S^2_n/\delta^2 (\bar{X}_n)}$ where ${s^2_n}$ and ${\bar{X}_n}$ are the sequences of sample variance and sample mean of the independently and identically distributed (i.i.d.) random variables with distribution $F_{\theta}(x), \theta \in \Theta$, respectively, and $\delta$ is either constant or any given positive real valued function. We obtain some asymptotic normality and asymptotic expectation of the N(c) in various limiting situations. Specially, uniform asymptotic normality and uniform asymptotic expectation of the N(c) are given.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.609-621
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• 2007

Diagnostic test results, which are approximately normal with a few number of outliers, but non-normal probability distribution, are frequently observed in practice. In the evaluation of two diagnostic tests, Greenhouse and Mantel (1950) proposed a parametric test under the assumption of normality but this test is inappropriate for the above non-normal case. In this paper, we propose a computationally simple nonparametric test that is based on quantile estimators of mean and standard deviation, instead of the moment-based mean and standard deviation as in some parametric tests. Parametric and nonparametric tests are compared with simulations under the assumption of, respectively, normality and non-normality, and under various combinations of the probability distributions for the normal and diseased groups.

• Proceedings of the Safety Management and Science Conference
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• 2012.04a
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• pp.579-583
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• 2012

The Design of Experiment (DOE) is a most practical technique when establishing an optimal condition for production technology in Six Sigma innovation project. This research proposes the assessment of properties of error terms, such as normality, equal variance, unbiasedness and independence. The properties of six nonparametric ranking techniques for checking normality assumption are discussed as well as run test which is used to identify the randomness, and to check unbiased assumption. Furthermore, Durbin-Watson (DW) statistics and ARIMA (p,d,q) process are discussed to identify the serial correlation.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.195-205
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• 2005

In decision tree analysis, C4.5 and CART algorithm have some problems of computational complexity and bias on variable selection. But QUEST algorithm solves these problems by dividing the step of variable selection and split point selection. When input variables are continuous, QUEST algorithm uses ANOVA F-test under the assumption of normality and homogeneity of variances. In this paper, we investigate the influence of violation of normality assumption and effect of the transformation of variables in the QUEST algorithm. In the simulation study, we obtained the empirical powers of variable selection and the empirical bias of variable selection after transformation of variables having various type of underlying distributions.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.429-436
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• 1999

We suggest test statistics for normality using Q-Q plot and P-P plot and obtain empirical quantities of these statistics. Also the power comparison with Shapiro-Wilk's W is conducted by Monte Carlo study.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1399-1412
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• 2016

We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.