• The Korean Journal of Applied Statistics
• /
• v.12 no.1
• /
• pp.153-163
• /
• 1999

경제학분야에서 소득분배의 불균형 정도에 대한 척도로 널리 이용되는 Lorenz curve를 소개하고, 변환에 의한 Lorenz curve기법을 도입하여 통계학의 주요 주제인 모집단의 분포에 대한 추정에 적용할 수 있는지 조사한다. 여러 특정분포에 대한 변환된 Lorenz curve의 특징을 제시하고 예제로 Hodgkin’s disease 데이터를 이용하여 Q-Q 플롯과 새로 제시한 변환된 Lorenz curve를 비교한다.

• Journal of the Korean Statistical Society
• /
• v.35 no.3
• /
• pp.305-316
• /
• 2006

Absolute Lorenz curve plays an important role for measuring absolute income inequality. Properties of absolute Lorenz curve are listed. Asymptotically distribution free and consistent tests have been proposed for comparing two absolute Lorenz curves in the whole interval [P1, P2] where 0 < P1 < P2 < 1. Absolute Lorenz ordering has been discussed for some distributions.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.3
• /
• pp.653-660
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.185-192
• /
• 2001

Using the Lorenz curve that is proved to be a powerful tool to measure the income inequality within a population of income receivers, we propose the normalized sample Lorenz curve for the goodness-of-fit test that is very important test in statistical analysis. For two hodgkin's disease data sets, we compare the Q-Q plot and the proposed normalized sample Lorenz curve.

• The Korean Journal of Applied Statistics
• /
• v.15 no.2
• /
• pp.415-421
• /
• 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 Korean Society of Forest Science
• /
• v.86 no.2
• /
• pp.158-166
• /
• 1997

This study presents the method to quantify the stand structure diversity or homogeneity. Gadow's dbh differentiation(Durchmesserdifferenzierung) is introduced which quantifies the horizontal stand structure by the ratio of the dbh between subject tree and neighbour trees. And new stand structure diversity index based on Lorenz curve, which is made by ratio of tree number and basal area or volume by dbh class, is presented. The horizontal stand structure index based on Lorenz curve has a value from 0 to 1 as Gadow's index, and approximates to 1 if the stand structure has high diversity. In the comparative analysis for performance, the new stand structure index based on Lorenz curve is considered to compare with the Gadow's index for describing the stand structure.

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

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.249-256
• /
• 2001

We shall derive the MLE and UMVUE of Lorenz Curve and Gini Index in a Pareto distribution with the pdf(1.1) and their variances. And compare mean square errors(MSE) of the MLE and UMVUE of the Lorenz Curve and Gini Index in a Pareto distribution with pdf(1.1).

• Communications for Statistical Applications and Methods
• /
• v.7 no.1
• /
• pp.277-284
• /
• 2000

The transformed sample Lorenz curve provides a powerful and easily computed goodness-of-fit test for exponentiality which does not depend on the unknown scale parameter. We compare the power of the transformed sample Lorenz curve statistic with the other goodness-of-fit tests for exponentiality against various alternatives through Monte Carlo methods and discuss the results.

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