• Title/Summary/Keyword: Shapiro-Wilk 통계량

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An Approximate Shapiro -Wilk Statistic for Testing Multivariate Normality (다변량 정규성검정을 위한 근사 SHAPIRO-WILK 통계량의 일반화)

  • 김남현
    • The Korean Journal of Applied Statistics
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    • v.17 no.1
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    • pp.35-47
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    • 2004
  • In this paper, we generalizes Kim and Bickel(2003)'s statistic for bivariate normality to that of multinormality, applying Fattorini(1986)'s method. Fattorini(1986) generalized Shapiro-Wilk's statistic for univariate normality to multivariate cases. The proposed statistic could be considered as an approximate statistic to Fattorini(1986)'s. It can be used even for a big sample size. Power performance of the proposed test is assessed in a Monte Carlo study.

The Shapiro-Wilk Type Test for Exponentiality Based on Progressively Type II Censored Data (전진 제 2종 중도절단자료에 대한 Shapiro-Wilk 형태의 지수검정)

  • Kim, Nam-Hyun
    • The Korean Journal of Applied Statistics
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    • v.23 no.3
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    • pp.487-495
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    • 2010
  • This paper develops a goodness of fit test statistic to test if the progressively Type II censored sample comes from an exponential distribution with origin known. The test is based on normalizing spacings and Stephens (1978)' modified Shapiro and Wilk (1972) test for exponentiality. The modification is for the case where the origin is known. We applied the same modification to Kim (2001a)'s statistic, which is based on the ratio of two asymptotically efficient estimates of scale. The simulation results show that Kim (2001a)'s statistic has higher power than Stephens' modified Shapiro and Wilk statistic for almost all cases.

A Modification of the Shapiro-Wilk Test for Exponentiality Based on Censored Data (중도절단자료에 대한 수정된 SHAPIRO-WILK 지수 검정)

  • Kim, Nam-Hyun
    • The Korean Journal of Applied Statistics
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    • v.21 no.2
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    • pp.265-273
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    • 2008
  • Kim (2001a) presented a modification of the Shapiro and Wilk (1972) test for exponentiality based on the ratio of two asymptotically efficient estimates of scale. In this paper we modify this test statistic when the sample is censored. We use the normalized spacings based on the sample data, which was used in Samanta and Schwarz (1988) to modify the Shapiro and Wilk (1972) statistic to the censored data. As a result the modified statistics have the same null distribution as the uncensored case with a corresponding reduction in sample size. Through a simulation study it is found that the proposed statistic has higher power than Samanta and Schwarz (1988) statistic especially for the alternatives with the coefficient of variation greater than or equal to 1.

다변량 정규성검정을 위한 근사 SHAPIRO-WILK 통계량의 일반화

  • Kim, Nam-Hyeon
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.05a
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    • pp.243-248
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    • 2003
  • Fattorini(1986)의 통계량은 Shapiro와 Wilk의 일변량 정규분포를 위한 검정통계량을 다변량으로 확장한 것이다. 본 논문에서는 Kim과 Bickel(2003)에서 제안한 이변량 정규분포를 위한 검정통계량을 Fattorini(1986)의 방법을 이용하여 이변량 이상인 경우에도 실제적으로 사용가능하도록 일반화하였다. 제안된 통계량은 Fattorini(1986) 통계량의 근사통계량으로 생각할 수 있으며 표본의 크기가 클 때도 사용가능하다.

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Power Analysis for Normality Plots (정규성 그래프의 검정력 비교)

  • Lee, Jae-Young;Rhee, Seong-Won
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.429-436
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    • 1999
  • We suggest test statistics for normality using Q-Q plot and P-P plot and obtain empirical quantities of these statistics. Also the power comparison with Shapiro-Wilk's W is conducted by Monte Carlo study.

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Q-Q, P-P 플롯의 변동 통계량에 대한 ROC 분석

  • 이제영;이성원
    • Communications for Statistical Applications and Methods
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    • v.5 no.1
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    • pp.205-215
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    • 1998
  • 정규분포에 관한 검정에 있어서 P-P 플롯과 Q-Q 플롯의 가시적인 변동을 이용한 통계량을 제시하고 이 통계량들과 Shapiro-Wilk의 W 통계량과의 비교를 정확도(accuracy)의 측면을 고려하여 실시하였다. 또한, 의학이나 임상에서 척도의 우수성을 검정하기 위해 많이 사용하는 Receiver Operating Characteristic (ROC) 분석 기법을 이용하여 제시된 통계량들에 관한 Power와 Accuracy는 물론 Best Cut-Off 측면에서의 효율성을 검정하였다.

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지수분포의 검정을 위한 수정된 W-통계량

  • 김남현
    • Proceedings of the Korean Statistical Society Conference
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    • 2000.11a
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    • pp.141-146
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    • 2000
  • Shapiro와 Wilk(1972)는 위치모수와 척도모수가 미지인 경우 지수분포의 검정통계량을 제안하였다. 그것은 척도모수의 일반화 최소제곱추정량과 표본분산의 비로 구성되었다. 그러나 이 검정통계량은 일치성을 갖지 않는다. 본 논문에서는 척도모수의 두개의 점근유효추정량으로 구성된 통계량을 고려하고 이의 극한분포를 구하였다. 또한 두 개의 통계량의 검정력을 비교한 결과 제안된 통계량이 변동계수가 1보다 크거나 같은 분포에서 더 좋은 검정력을 가짐을 볼 수 있었다.

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More Powerful Test for Normality Based on the Normalized Sample Lorenz Curve (NORMALIZED SAMPLE LORENZ CURVE를 이용한 검정력이 높은 정규성 검정)

  • 강석복;조영석
    • 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.

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.

Detecting the Climate Factors related to Dry Matter Yield of Whole Crop Maize (사일리지용 옥수수의 건물수량에 영향을 미치는 기후요인 탐색)

  • Peng, Jing-lun;Kim, Moon-ju;Kim, Young-ju;Jo, Mu-hwan;Nejad, Jalil Ghassemi;Lee, Bae-hun;Ji, Do-hyeon;Kim, Ji-yung;Oh, Seung-min;Kim, Byong-wan;Kim, Kyung-dae;So, Min-jeong;Park, Hyung-soo;Sung, Kyung-il
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.17 no.3
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    • pp.261-269
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    • 2015
  • The purpose of this research is to identify the significance of climate factors related to the significance of change of dry matter yield (DMY) of whole crop maize (WCM) by year through the exploratory data analysis. The data (124 varieties; n=993 in 7 provinces) was prepared after deletion and modification of the insufficient and repetitive data from the results (124 varieties; n=1027 in 7 provinces) of import adaptation experiment done by National Agricultural Cooperation Federation. WCM was classified into early-maturity (25 varieties, n=200), mid-maturity (40 varieties, n=409), late-maturity (27 varieties, n=234) and others (32 varieties, n=150) based on relative maturity and days to silking. For determining climate factors, 6 weather variables were generated using weather data. For detecting DMY and climate factors, SPSS21.0 was used for operating descriptive statistics and Shapiro-Wilk test. Mean DMY by year was classified into upper and lower groups, and a statistically significant difference in DMY was found between two groups (p<0.05). To find the reasons of significant difference between two groups, after statistics analysis of the climate variables, it was found that Seeding-Harvesting Accumulated Growing Degree Days (SHAGDD), Seeding-Harvesting Precipitation (SHP) and Seeding-Harvesting Hour of sunshine (SHH) were significantly different between two groups (p<0.05), whereas Seeding-Harvesting number of Days with Precipitation (SHDP) had no significant effects on DMY (p>0.05). These results indicate that the SHAGDD, SHP and SHH are related to DMY of WCM, but the comparison of R2 among three variables (SHAGDD, SHP and SHH) couldn't be obtained which is needed to be done by regression analysis as well as the prediction model of DMY in the future study.