• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.309-316
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• 2014

Testing normality is very important because the most common assumption is normality in statistical analysis. We propose a new plot and test statistic to goodness-of-fit test for normality based on the generalized Lorenz curve. We compare the new plot with the Q-Q plot. We also compare the new test statistic with the Kolmogorov-Smirnov (KS), Cramer-von Mises (CVM), Anderson-Darling (AD), Shapiro-Francia (SF), and Shapiro-Wilks (W) test statistic in terms of the power of the test through by Monte Carlo method. As a result, new plot is clearly classified normality and non-normality than Q-Q plot; in addition, the new test statistic is more powerful than the other test statistics for asymmetrical distribution. We check the proposed test statistic and plot using Hodgkin's disease data.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.41-52
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• 2006

Because most common assumption is normality in statistical analysis, testing normality is very important. The Q-Q plot is a powerful tool to test normality with full samples in statistical package. But the plot can't test normality in type-II censored samples. This paper proposed the modified the Q-Q plot and the modified normalized sample Lorenz curve(NSLC) for normality test in the type-II censored samples. Using the two Hodgkin's disease data sets and the type-II censored samples, we picture the modified Q-Q plot and the modified normalized sample Lorenz curve.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.115-122
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• 2006

A test is suggested for detecting deviations from both multivariate normality and independence. This test can be used for assessing the normality and independence of univariate time series residuals. We derive the limiting distribution of the test statistic and a simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we apply our method to a real data of time series.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1191-1200
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. 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 two non-normal distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.203-212
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• 2006

A chi-squared test of multivariate normality is suggested which is mainly focused on detecting deviations from elliptical symmetry. This test uses Mahalanobis distances of observations to have some power for deviations from multivariate normality. We derive the limiting distribution of the test statistic by a conditional limit theorem. 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 two non-normal distributions.

• 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.20 no.2
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• pp.453-458
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• 2009

In this paper, we consider Jarque-Bera (JB) normality test for the innovations of ARMA-GARCH models. In financial applications, JB test based on the residuals are routinely used for the normality of ARMA-GARCH innovations without a justification. However, the validity of JB test should be justified in advance of the actual practice (Lee et al., 2009). Through the simulation study, it is found that the validity of JB test depends on the shape of test statistic. Specifically, when the constant term is involved in ARMA model, a certain type of residual based JB test produces severe size distortions.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.851-858
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• 2001

Using the normalized sample Lorenz curve which is introduced by Kang and Cho (2001), we propose the test statistics for testing of normality that is very important test in statistical analysis and compare the proposed test with the other tests in terms of the power of test through by Monte Carlo method. The proposed test is more power than the other tests except some cases

• Journal of Environmental Health Sciences
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• v.45 no.2
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• pp.192-202
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• 2019

Objectives: According to the central limit theorem, the samples in population might be considered to follow normal distribution if a large number of samples are available. Once we assume that toxicity dataset follow normal distribution, we can treat and process data statistically to calculate genus or species mean value with standard deviation. However, little is known and only limited studies are conducted to investigate whether toxicity dataset follows normal distribution or not. Therefore, the purpose of study is to evaluate the generally accepted normality hypothesis of aquatic toxicity dataset Methods: We selected the 8 chemicals, which consist of 4 organic and 4 inorganic chemical compounds considering data availability for the development of species sensitivity distribution. Toxicity data were collected at the US EPA ECOTOX Knowledgebase by simple search with target chemicals. Toxicity data were re-arranged to a proper format based on the endpoint and test duration, where we conducted normality test according to the Shapiro-Wilk test. Also we investigated the degree of normality by simple log transformation of toxicity data Results: Despite of the central limit theorem, only one large dataset (n>25) follow normal distribution out of 25 large dataset. By log transforming, more 7 large dataset show normality. As a result of normality test on small dataset (n<25), log transformation of toxicity value generally increases normality. Both organic and inorganic chemicals show normality growth for 26 species and 30 species, respectively. Those 56 species shows normality growth by log transformation in the taxonomic groups such as amphibian (1), crustacean (21), fish (22), insect (5), rotifer (2), and worm (5). In contrast, mollusca shows normality decrease at 1 species out of 23 that originally show normality. Conclusions: The normality of large toxicity dataset was not always satisfactory to the central limit theorem. Normality of those data could be improved through log transformation. Therefore, care should be taken when using toxicity data to induce, for example, mean value for risk assessment.