• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.221-231
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• 2006

A chi-squared test of multivariate normality is suggested which is oriented for detecting deviations from elliptical symmetry. We derive the limiting distribution of the test statistic via a central limit theorem on empirical processes. A simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we compare the power of our method with those of other popular tests of multivariate normality under a non-normal distribution.

• 한국물환경학회지
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• 제21권6호
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• pp.651-658
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• 2005

The Non-parametric Analysis is powerful in data test especially for the non- normality water quality data. The data at three monitoring stations of the Tam-Jin River were evaluated for their normality using Skewness, Q-Q plot and Shapiro-Willks tests. Various constituent of water quality data including temperature, pH, DO, SS, BOD, COD, TN and TP in the period of January 1994 to December 2004 were used as dataset. Shapiro-Willks normality test was carried out for a test 5% significance level. Most water quality data except DO at monitoring stations 1 and 2 showed that data does not normally distributed. It is indicating that non-parametric method must be used for a water quality data. Therefore, a homogeneity was conducted by Mann-Whitney U test (p<0.05). Two stations were paired in three pairs of such stations. Differences between stations 1, 2 and stations 1, 3 for pH, BOD, COD, TN and TP were meaningful, but Tam-Jin 2 and 3 stations did not meaningful. In addition, a narrow gap of the water quality ranges is not a difference. Categories in which all three pairs of stations (1 and 2, 2 and 3, 1 and 3) in the Tam-Jin River showed difference in water quality were analyzed on TN and TP. The results of in this research suggest a right analysis in the homogeneity test of water quality data and a reasonable management of pollutant sources.

• 대한수학회보
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• 제51권3호
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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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• 제15권2호
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• pp.161-171
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• 2008

This study discusses Johnson's $S_U$-normal distribution capturing a wide range of non-normality in various regression models. We provide the likelihood inference using Johnson's $S_U$-normal distribution, and propose a likelihood ratio (LR) test for normality. We also apply the $S_U$-normal distribution to the binary and censored regression models. Monte Carlo simulations are used to show that the LR test using the $S_U$-normal distribution can be served as a model specification test for normal error distribution, and that the $S_U$-normal maximum likelihood (ML) estimators tend to yield more reliable marginal effect estimates in the binary and censored model when the error distributions are non-normal.

• 응용통계연구
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• 제25권5호
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• pp.803-811
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• 2012

For credit evaluation models, we extend the study of discriminatory power based on AUC obtained from a ROC curve when the number of defaults is small and distribution functions of the defaults and non-defaults are normal distributions. Since distribution functions do not satisfy normality in real world, the distribution functions of the defaults and non-defaults are assumed as normal mixture distributions based on results that the normal mixture could be better fitted than other distribution estimation methods for non-normal data. By using several AUC statistics, the discriminatory power under such a circumstance is explored and compared with those of normal distributions.

• 대한조선학회논문집
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• 제55권6호
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• pp.466-473
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• 2018

Most frequency domain-based approaches assume that structural response should be a Gaussian random process. But a lot of non-Gaussian processes caused by multi-excitation and non-linearity in structural responses or load itself are observed in many real engineering problems. In this study, the effect of non-Normality on fatigue damages are discussed through case study. The accuracy of four frequency domain methods for non-Gaussian processes are compared in the case study. Power-law and Hermite models which are derived for non-Gaussian narrow-banded process tend to estimate fatigue damages less accurate than time domain results in small kurtosis and in case of large kurtosis they give conservative results. Weibull model seems to give conservative results in all environmental conditions considered. Among the four methods, Benascuitti-Tovo model for non-Gaussian process gives the best results in case study. This study could serve as background material for understanding the effect of non-normality on fatigue damages.

• 융합신호처리학회논문지
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• 제20권4호
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• pp.193-198
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• 2019

인터넷상에서의 진짜 및 가짜 정보의 범람이 수많은 텍스트 분석에 대한 연구를 이끌었다. 문헌 표기 없이 타인의 저작물을 무단 복제 및 관련 없는 연구결과 조작 등이 한동안 세간의 주목을 이끌었다. 연구 분야에서 표절과 이의 대항 및 감소를 위해 다양한 도구들이 개발되었다. Pearson Spearman 본 연구에서는 코사인 유사성과 및 상관관계를 이용하는 파라미터 및 비 파라미터 방법을 이용하여 문장 유사성을 측정한다. Pearson 코사인 유사성과 상관관계는 가장 높은 유사성 계수를 얻었으나 Spearman 상관관계는 낮은 유사성 계수를 보여주었다. 본 논문에서는 정상성 가정과 편향성에 의존하는 파라미터 방법들에 반하도록 비정상성 가정으로 인한 문장 유사도를 측정하는 데 있어 비 파라미터 방법들을 사용하는 것을 제안한다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.3-9
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• 2002

In financial time series, the autoregressive conditional heteroscedastic (ARCH) models have been widely used for modeling conditional variances. In many cases, non-normality or heavy-tailed distributions of the data have influenced the estimation methods under normality assumption. To solve this problem, a robust function for the conditional variances of the errors is proposed and compared the relative efficiencies of the estimators with other conventional models.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.91-97
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• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.265-272
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• 2002

An Integer-valued autoregressive integrated (INARI) model is introduced to eliminate stochastic trend and seasonality from time series of count data. This INARI extends the previous integer-valued ARMA model. We show that it is stationary and ergodic to establish asymptotic normality for conditional least squares estimator. Optimal estimating equations are used to reflect categorical and serial correlations arising from panel count data and variations arising from three random processes for obtaining observation into estimation. Under regularity conditions for martingale sequence, we show asymptotic normality for estimators from the estimating equations. Using cancer mortality data provided by the U.S. National Center for Health Statistics (NCHS), we apply our results to estimate the probability of cells classified by 4 causes of death and 6 age groups and to forecast death count of each cell. We also investigate impact of three random processes on estimation.