• 한국전자통신학회논문지
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• 제6권2호
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• pp.193-198
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• 2011

행렬들 중 그것의 성분으로 부호인 + 와 0 만을 갖는 행렬을 우리는 비음인 부호화 행렬이라 한다. 또한 비음인 부호화 행렬 A가 그것과 같은 부호를 갖는 실수 정규행렬 B가 존재하면 정규성을 허용한다고 한다. 본 논문은 참고문헌[1] 에서 밝힌 형태와 다른 특별한 형태를 조사했고, 실수 행렬 중 비음인 정규행렬을 구성하는 흥미로운 방법을 제공했다.

• 응용통계연구
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• 제17권3호
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• pp.507-518
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• 2004

Malkovich & Afifi (1973)는 합교원리 (union-intersection principle)를 이용하여 왜도와 첨도를 다변량으로 일반화하였으나 이는 자료의 차원이 클 경우에는 사용이 용이하지 않다. 본 논문에서는 이러한 단점을 보완하는 이들의 근사통계량을 제안한다. 그리고 제안된 근사통계량, Malkovich & Afifi (1973)의 통 계 량, Mardia(1970)의 왜도와 첨도의 검 정력을 모의실험을 통하여 비교한다.

• Communications for Statistical Applications and Methods
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• 제27권5호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제41권1호
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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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• 제24권2호
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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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• 제14권3호
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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.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2012년 춘계학술대회
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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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• 제16권2호
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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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• 제10권2호
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• pp.429-436
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• 1999

정규분포에 관한 검정에 있어서 P-P 플롯과 Q-Q 플롯에서 정규분포에서의 기대 직선의 잔차들을 이용한 두 가지 통계량을 제시하고, 이 통계량들의 경험적 분위수(empirical quantile)를 구하였다. 그리고 이들 통계량의 검정력을 Shapiro-Wilk의 W 통계량과의 비교를 통하여 분석하였다.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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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.