• Title/Summary/Keyword: test of normality

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An Improved Quantize-Quantize Plot for Normality Test

  • Lee, Jea-Young;Rhee, Seong-Won
    • Communications for Statistical Applications and Methods
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    • v.5 no.1
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    • pp.67-75
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    • 1998
  • A new graphical method, named transformed quantize-quantile (TQQ), of a quantize-quantile (Q-Q) Plot is developed for the detection of deviations from the normal distribution. It will be shown that TQQ is helpful for detecting patterns of how points depart from normality. TQQ characteristics of the various kinds of representations are illustrated by a generated sample from a composite of a normal distribution and a clinical example for TQQ is constructed and explained.

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Weak Convergence of U-empirical Processes for Two Sample Case with Applications

  • Park, Hyo-Il;Na, Jong-Hwa
    • Journal of the Korean Statistical Society
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    • v.31 no.1
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    • pp.109-120
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    • 2002
  • In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.

A Study on Split Variable Selection Using Transformation of Variables in Decision Trees

  • Chung, Sung-S.;Lee, Ki-H.;Lee, Seung-S.
    • 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.

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Testing Multivariate Normality Based on EDF Statistics (EDF 통계량을 이용한 다변량 정규성검정)

  • Kim Nam-Hyun
    • The Korean Journal of Applied Statistics
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    • v.19 no.2
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    • pp.241-256
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    • 2006
  • We generalize the $Cram{\acute{e}}r$-von Mises Statistic to test multivariate normality using Roy's union-intersection principle. We show the limit distribution of the suggested statistic is representable as the integral of a suitable Gaussian process. We also consider the computational aspects of the proposed statistic. Power performance is assessed in a Monte Carlo study.

Remarks on the Use of Multivariate Skewness and Kurtosis for Testing Multivariate Normality (정규성 검정을 위한 다변량 왜도와 첨도의 이용에 대한 고찰)

  • 김남현
    • 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.

A Rao-Robson Chi-Square Test for Multivariate Normality Based on the Mahalanobis Distances

  • Park, Cheolyong
    • Communications for Statistical Applications and Methods
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    • v.7 no.2
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    • pp.385-392
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    • 2000
  • Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

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Suspended Particulate Concentration at the Drilling Site of Underground Coal Mines in Taebaek Area (태백지역 석탄광업 굴진부서의 부유분진 농도)

  • 윤영노;김영식;이영신
    • Journal of Environmental Health Sciences
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    • v.17 no.1
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    • pp.32-38
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    • 1991
  • Airborne suspended particulate concentration in drilling sites of underground coal mines in Taebaek area was evaluated. And respirable coal dust exposure level was evaluated. Airborne suspended particulate mass include total suspended particle(TSP) and thoracic particle(TPM). TSP (by open-face filter holder) and TPM(by elutriator) concentration were determined by low volume air samplers. Personal air samplers were attached to the coal workers including drillers, coal cutters, and their assistants. Normality and log-normality of TSP, TPM, and respirable dust(RPM) concentration were tested by Kolmogorov-Smirnov one-sample test. Differences of means of TSP, TPM, and RPM concentration were tested by paired t-test. Relation between TSP, TPM, and RPM with pairs were tested by regression test and Pearson's correlation.

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Testing Log Normality for Randomly Censored Data (임의중도절단자료에 대한 로그정규성 검정)

  • Kim, Nam-Hyun
    • The Korean Journal of Applied Statistics
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    • v.24 no.5
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    • pp.883-891
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    • 2011
  • For survival data we sometimes want to test a log normality hypothesis that can be changed into normality by transforming the survival data. Hence the Shapiro-Wilk type statistic for normality is generalized to randomly censored data based on the Kaplan-Meier product limit estimate of the distribution function. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version under the simpl hypothesis. These two test statistics are compared through a simulation study. As for the distribution of censoring variables, we consider Koziol and Green (1976)'s model and other similar models. Through the simulation results, we can see that the power of the proposed statistic is higher than that of Koziol-Green statistic and that the proportion of the censored observations (rather than the distribution of censoring variables) has a strong influence on the power of the proposed statistic.

Testing the Equality of Several Correlation Coefficients by Permutation Method

  • Um, Yonghwan
    • Journal of the Korea Society of Computer and Information
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    • v.27 no.6
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    • pp.167-174
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    • 2022
  • In this paper we investigate the permutation test for the equality of correlation coefficients in several independent populations. Permutation test is a non-parametric testing methodology based upon the exchangeability of observations. Exchangeability is a generalization of the concept of independent, identically distributed random variables. Using permutation method, we may construct asymptotically exact test. This method is asymptotically as powerful as standard parametric tests and is a valuable tool when the sample sizes are small and normality assumption cannot be met. We first review existing parametric approaches to test the equality of correlation coefficients and compare them with the permutation test. At the end, all the approaches are illustrated using Iris data example.

Test for Trend Change in NBUE-ness Using Randomly Censored Data

  • Dae-Kyung Kim;Dong-Ho Park;June-Kyun Yum
    • Communications for Statistical Applications and Methods
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    • v.2 no.2
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    • pp.1-12
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    • 1995
  • Let F be a life distribution with finite mean $\mu$ Then F is said to be in new better then worse than used in expectation (NBWUE(p)) class if $\varphi(u) {\geq} u$ for $0 {\leq}u{\leq}t_0$ and ${\varphi}(u) {\leq} u$ for $t_0< u {\leq} 1$ where ${\varphi}(u)$ is the scaled total-time-on-test transform and $p=F(t_0)$. We propose a testing procedure for $H_0$ : F is exponential against $H_1$ : NBWUE(p), and is not expontial, (or $H_1\;'$ : F is NWBUE (p), and is not exponential) using randomly censored data. Our procedure assumes kmowledge of the proportion p of the population that fail at or before the change-point $\t_0$. Know ledge of $\t_0$ itself is not assumed. The asymptotic normality of the test statistic is established and a Monte Carlo experiment is performed to investigate the speed of convergence of the test statistic to normality. The power of our test is also studied.

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