Modification of Anderson-Darling goodness-of-fit test for normality PDF

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Modification of Anderson-Darling goodness-of-fit test for normality

Critical values of the ADm test are determined by a. Monte Carlo simulation for sample sizes . The ADm test was compared with the other normality tests with.

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Modification of Anderson-Darling goodness-of-fit test for normality

270 | AFINIDAD LXXVI, 588

Correspondig author: piotr.sulewski@apsl.edu.pl

Modification of Anderson-Darling

goodness-of-flt test for normality

P. Sulewski

The Pomeranian University in Słupsk, Institute of Mathematics, Poland Modificación del test de bondad de ajuste de Anderson-Darling para normalidad

Modiflcació del test de bondat d'ajustament de Anderson-Darling per a la normalitatRECEIVED: 30 JANUARY 2019; REVISED: 11 APRIL 2019; ACCEPTED: 6 MAY 2019

SUMMARY

?e objective of the paper is to present a new good- ness-of-flt test for normality. fiis new proposition, here called the ADm test, is a modiflcation of the Anderson-Darling goodness-of-flt test for normality. Critical values of the ADm test are determined by a

Monte Carlo simulation for sample sizes . fie ADm

test was compared with the other normality tests with respect to their power. fie simulation study shows

that the ADm test is the most powerful for symmetric short tailed distributions and for symmetric distribu- tions close to the normal distribution. fie test has also the best performance for asymmetric short tailed distributions.

Key words: Anderson-Darling test, empirical dis-

tribution function, goodness-of-flt tests, Monte Carlo simulation, tests for normality.

RESUMEN

El objetivo del informe es presentar un test nuevo de bondad de ajuste para normalidad. Esta nueva pro- puesta, conocida aquí como prueba de ADm es una modiflcación del test o prueba de bondad de ajuste de Anderson-Darling para normalidad. Los valores críticos del test de ADm son determinados por una

simulación Monte Carlo para tamaños de muestra . El test ADm se ha comparado con otros tests de nor-

malidad en lo que se reflere a su potencia. El estudio de simulación demuestra que el test ADm es el más potente para distribuciones simétricas de cola corta y para distribuciones simétricas próximas a la distribu- ción normal. El test muestra también el mayor rendi- miento para distribuciones asimétricas de cola corta.

Palabras clave: Prueba de Anderson-Darling, fun-

ción de distribución empírica, pruebas o tests de bon- dad de ajuste, simulación de Monte Carlo, pruebas de normalidad. RESUM L'objectiu del informe es presentar un test nou de bondat d'ajustament per a la normalitat. Aquesta nova proposta, coneguda aquí como test de ADm es una

modiflcació del test o prova de bondat d'ajustament de Anderson-Darling per a la normalitat. Els valors crítics

del test de ADm son determinats per una simulació Monte Carlo per volums de mostra . El test ADm s'ha comparat amb altres tests de normalitat en el que es refereix a la seva potencia. El estudi de simulació de- mostra que el test ADm es el mes potent per distri- bucions simètriques de cua curta i per distribucions

simètriques pròximes a la distribució normal. El test mostra també el major rendiment per a distribucions

asimètriques de cua curta. Paraules clau: Prova de Anderson-Darling, funció de distribució empírica, proves o tests de bondat d'ajusta- ment, simulació de Monte Carlo, proves de normalitat.

OCTOBER ? DECEMBER 2019 | 271

INTRODUCTION

Doubtlessly the most common packet of statistical

inference procedures deals parameters of the Normal distributions. However, before an analyst uses one of these procedures he has to check whether empir- ical data come from general population in which the Normal distribution "is in force". In other words, the analyst is obliged to perform a goodness-of-flt test (GoFT). fiis paper is devoted to the Anderson - Dar- ling GoFT and its modiflcation. fie following notation will be used throughout the paper:

NotationDescriptionNotationDescription

GoFTGoodness-of-?t testKSKolmogorov-Smirnov

PDFProbability density functionNDNormal distribution

CDFCumulative distribution

function

SWShapiro-Wilk

EDFEmpirical distribution functionPDF of ND

LFLillieforsEDF

ADAnderson-DarlingCDF of ND

ADmModi?ed Andreson-DarlingcvCritical value

?ere are many normality tests discussed in the sta- tistical literature. However, the most common nor-quotesdbs_dbs2.pdfusesText_2

[PDF] Modification of Anderson-Darling goodness-of-fit test for normality

goftest: Classical Goodness-of-Fit Tests for Univariate Distributions