• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.809-815
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• 2007

Since Bollerslev(1986), the GARCH model has been popular in analysing the volatility of the financial time series. In real data analysis, practitioners conventionally put the normal assumption on the innovation random variables of the GARCH model, which is often violated. In this paper, we analyse the domestic financial data based on the GARCH(1,1) model and among existing normality tests, perform the Jarque-Bera test based on the residuals. It is shown that the innovation based on the GARCH(1,1) model dose not follow the normality assumption.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.361-375
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• 2015

A measure of skewness and kurtosis is proposed to test multivariate normality. It is based on an empirical standardization using the scaled residuals of the observations. First, we consider the statistics that take the skewness or the kurtosis for each coordinate of the scaled residuals. The null distributions of the statistics converge very slowly to the asymptotic distributions; therefore, we apply a transformation of the skewness or the kurtosis to univariate normality for each coordinate. Size and power are investigated through simulation; consequently, the null distributions of the statistics from the transformed ones are quite well approximated to asymptotic distributions. A simulation study also shows that the combined statistics of skewness and kurtosis have moderate sensitivity of all alternatives under study, and they might be candidates for an omnibus test.

• Clinical and Experimental Reproductive Medicine
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• v.27 no.2
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• pp.191-200
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• 2000

Objective: This study was carried out to compare the effects of the stepwise exposure treatments on the morphological normality, fertilization and blastocyst formation rate of the frozen-thawed mouse mature oocytes by vitrification or ultra-rapid freezing and to use as a fundamental data for the cryopreservation of human oocytes. Materials and Methods: The morphological normality and fertilization rates of the vitrified and ultra-rapid frozen mouse mature oocytes after three-stepwise exposure treatments (1step, 3step and 5step) were observed. After choosing the 3step exposure treatment groups, we observed the morphological normality and fertilization, blastocyst formation rate of the vitrified and ultra-rapid frozen mouse mature oocytes. Results: The morphological normality and fertilization rates of the vitrified mouse mature oocytes after three-stepwise exposure treatments (1step, 3step and 5step) were 75%, 85%, 88% and 58%, 61 %, 54% respectively. There were no significant differences among treatments(p>0.05). The morphological normality and fertilization rate of the control was 92% and 65%. There were no significant differences in fertilization rate among control and treatments (p>0.05). The morphological normality and fertilization rates of the ultra-rapid frozen mouse mature oocytes after three-stepwise exposure treatments (1step, 3step and 5step) were 83%, 83%, 84% and 75%, 63%, 56% respectively. There were no significant differences among treatments (p>0.05). The morphological normality and fertilization rate of the control was 95% and 67%. There were no significant differences among control and treatments (p>0.05). The morphological normality and fertilization rate of the vitrified or ultra-rapid frozen mouse mature oocytes after 3step exposure treatment were 69% and 75%, respectively. The blastocyst formation rate was 60% and 57%. The results did not differ significantly between vitrification and ultra-rapid freezing (p>0.05). Conclusion: As known in the above results, there were no significant differences in the fertilization and blastocyst formation rate of the frozen-thawed mouse mature oocytes by vitrification or ultra-rapid freezing among the control and treatments. It is suggested that vitrification and ultra-rapid freezing method were effective for the cryopreservation of mouse mature oocytes.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.373-383
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• 2003

We investigate a uniform local asymptotic normality for likelihood ratio processes based on an independent and identically distributed local asymptotic problem. Our tool is an empirical process theory.

• The Korean Journal of Applied Statistics
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• v.14 no.2
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• pp.223-231
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• 2001

다변량분석 기법을 위해서는 자료가 정규성(normality)가정을 만족해야한다. 본 연구에서는 GUI환경에서 일변량 및 다변량자료의 정규성검정, 이상치제거 및 변수변환을 하는 시스템을 Visual Basic 언어로서 구축하여 사용자들이 보다 편리하게 사용할 수 있음을 소개 하고자 한다.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.253-255
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• 2000

다변량분석 기법을 사용하기 위해서는 자료가 정규성(normality)가정을 만족해야한다. 본 연구에서는 GUI(graphic user interface)환경 하에서 일변량(univariate)과 다변량자료(multivariate data)의 정규성검정, 이상치(outliers)제거 및 변수변환(variable transformation)을 지원하는 시스템을 구축하여 사용자들이 보다 편리하게 사용할 수 있음을 소개 하고자 한다.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.691-700
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• 2014

We study normality for families of meromorphic functions which is related to an extended version of a Hayman's conjecture on value distribution, and prove several normality criteria for meromorphic functions and certain non-homogeneous differential polynomials.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.687-694
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• 1999

The goodness of fit statistics of normality plots are obtained using the Receiver Operating Characteristic(ROC) method. This work is intended to compare with Shapiro-Wilk W statistic. Wel will use and discuss an accuracy of the test and the best cut-off value which minimizes the sum of the type I and II error probabilities.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.151-163
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• 2019

The aim of this paper is to consider the categorical equivalence between crossed modules within groupoids and 2-groupoids; and then relate normality and quotient in these two categories.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.685-696
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• 2012

These days the interest of quality leads to the necessity of control charts for monitoring the process in various fields of practical applications. The $\overline{X}$ chart is one of the most widely used tools for quality control that also performs well under the normality of quality characteristics. However, quality characteristics tend to have nonnormal properties in real applications. Numerous recent studies have tried to find and explore the performance of $\overline{X}$ chart due to non-normality; however previous studies numerically examined the effects of non-normality and did not provide any theoretical justification. Moreover, numerical studies are restricted to specific type of distributions such as Burr or gamma distribution that are known to be flexible but can hardly replace other general distributions. In this paper, we approximate the false alarm rate(FAR) of the $\overline{X}$ chart using the Edgeworth expansion up to 1/n-order with the fourth cumulant. This allows us to examine the theoretical effects of nonnormality, as measured by the skewness and kurtosis, on $\overline{X}$ chart. In addition, we investigate the effect of skewness and kurtosis on $\overline{X}$ chart in numerical studies. We use a skewed-normal distribution with a skew parameter to comprehensively investigate the effect of skewness.