Goodness-of-Fit Test for the Normality based on the Generalized Lorenz Curve

Abstract

Abstract Testingnormalityisveryimportantbecausethemostcommonassumptionisnormalityinstatisticalanalysis.We propose a new plot and test statistic to goodness-of-fit test for normality based on the generalized Lorenzcurve. 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 clearlyclassified normality and non-normality than Q-Q plot; in addition, the new test statistic is more powerful than theother test statistics for asymmetrical distribution. We check the proposed test statistic and plot using Hodgkin’sdisease data.Keywords: Generalized Lorenz curve, goodness-of-fit, Lorenz curve, normality test, power. 1. Introduction Testing normality is very important because the most common assumption is normality in statisticalanalysis. Sonormalitywasresearchedcontinuouslybymanyscholars. Estimationofdatadistributionis used to histogram, Q-Q plot and P-P plot which uses a graph. In addition to using the graphicmethod, typical methods using the test statistic are the Kolmogorov-Smirnov test and Shapiro-Wilktest.ThisstudyproposesageneralizedLorenzcurve(GLC)teststatisticandagraphicalmethod,calledthe