• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.653-660
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• 2003

In this paper, we prove that the transformed sample Lorenz curve, normalized sample Lorenz curve, and the test statistics for testing of normality based on the normalized sample Lorenz curve and the modified Lorenz curve which were introduced by Kang and Cho (2001a, 2002) are location and scale invariant statistics.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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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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• 제19권4호
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• pp.1441-1448
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• 2008

We propose the modified quantile-quantile (Q-Q) plot using the approximate maximum likelihood estimators and the modified normalized sample Lorenz curve (NSLC) plot for the extreme value distribution based on multiply Type-II censored samples. Using two example data sets, we picture the modified Q-Q plot and the modified NSLC plot.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.349-361
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• 2009

In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• 응용통계연구
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• 제15권2호
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• pp.415-421
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• 2002

통계적분석에서 가장 대표적인 가정이 정규성 가정이므로 데이터의 정규성 검정은 매우 중요하다. 이 논문에서는 정규성 검정을 위해 경제학에서 소득분배의 불균형에 관한 척도로 널리 이용되는 Lorenz curve를 변형한 새로운 플롯과 검정통계량을 제시한다. 그리고 제한한 검정을 W검정 (Shapiro and Wilk (1965)), Lorenz curve를 이용한 TL검정(Kang and Cho (1999))과 몬테칼로 방법을 이용하여 검정력을 비교한다. 제안된 검정이 특별한 대립분포의 경우를 제외하고는 대부분 검정력이 높았다.

• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.195-209
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• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Journal of the Korean Data and Information Science Society
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• 제21권2호
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• pp.317-325
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• 2010

In this paper, we develop four modified empirical distribution function (EDF) type tests using approximate maximum likelihood estimators for the half-logistic distribution based on multiply Type-II censored samples. We also propose modified normalize sample Lorenz curve polt and new test statistics. We compare the above test statistics in the sense of the power for various censored samples. We present an example to illustrate this method.