A test for normality based on the empirical distribution function

In this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample sizes and different significance levels. We study and compare the power of forty selected normality...

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Detalles Bibliográficos
Autores: Torabi, Hamzeh, Montazeri, Narges H., Grané, Aurea
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/112737
Acceso en línea:https://hdl.handle.net/2117/112737
Access Level:acceso abierto
Palabra clave:Empirical distribution function
entropy estimator
goodness-of-fit tests
Monte Carlo simulation
Robust Jarque-Bera test
Shapiro-Francia test
SJ test
test for normality.
Classificació AMS::62 Statistics::62F Parametric inference
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
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spelling A test for normality based on the empirical distribution functionTorabi, HamzehMontazeri, Narges H.Grané, AureaEmpirical distribution functionentropy estimatorgoodness-of-fit testsMonte Carlo simulationRobust Jarque-Bera testShapiro-Francia testSJ testtest for normality.Classificació AMS::62 Statistics::62F Parametric inferenceÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàticaIn this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample sizes and different significance levels. We study and compare the power of forty selected normality tests for a wide collection of alternative distributions. The new proposal is compared to some traditionaltest statistics, such as Kolmogorov-Smirnov, Kuiper, Cramér-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarque-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achieved by the new test. Other findings derivedfrom the simulation study are that SJ and Robust Jarque-Bera tests are the most powerful ones for symmetric alternatives with support on the whole real line, whereas entropy-based tests are preferable for alternatives with support on the unit interval.Peer ReviewedInstitut d'Estadística de Catalunya20162016-06-1720182018-01-12journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/112737reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1127372026-05-27T15:37:01Z
dc.title.none.fl_str_mv A test for normality based on the empirical distribution function
title A test for normality based on the empirical distribution function
spellingShingle A test for normality based on the empirical distribution function
Torabi, Hamzeh
Empirical distribution function
entropy estimator
goodness-of-fit tests
Monte Carlo simulation
Robust Jarque-Bera test
Shapiro-Francia test
SJ test
test for normality.
Classificació AMS::62 Statistics::62F Parametric inference
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
title_short A test for normality based on the empirical distribution function
title_full A test for normality based on the empirical distribution function
title_fullStr A test for normality based on the empirical distribution function
title_full_unstemmed A test for normality based on the empirical distribution function
title_sort A test for normality based on the empirical distribution function
dc.creator.none.fl_str_mv Torabi, Hamzeh
Montazeri, Narges H.
Grané, Aurea
author Torabi, Hamzeh
author_facet Torabi, Hamzeh
Montazeri, Narges H.
Grané, Aurea
author_role author
author2 Montazeri, Narges H.
Grané, Aurea
author2_role author
author
dc.subject.none.fl_str_mv Empirical distribution function
entropy estimator
goodness-of-fit tests
Monte Carlo simulation
Robust Jarque-Bera test
Shapiro-Francia test
SJ test
test for normality.
Classificació AMS::62 Statistics::62F Parametric inference
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
topic Empirical distribution function
entropy estimator
goodness-of-fit tests
Monte Carlo simulation
Robust Jarque-Bera test
Shapiro-Francia test
SJ test
test for normality.
Classificació AMS::62 Statistics::62F Parametric inference
Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
description In this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample sizes and different significance levels. We study and compare the power of forty selected normality tests for a wide collection of alternative distributions. The new proposal is compared to some traditionaltest statistics, such as Kolmogorov-Smirnov, Kuiper, Cramér-von Mises, Anderson-Darling, Pearson Chi-square, Shapiro-Wilk, Shapiro-Francia, Jarque-Bera, SJ, Robust Jarque-Bera, and also to entropy-based test statistics. From the simulation study results it is concluded that the best performance against asymmetric alternatives with support on the whole real line and alternative distributions with support on the positive real line is achieved by the new test. Other findings derivedfrom the simulation study are that SJ and Robust Jarque-Bera tests are the most powerful ones for symmetric alternatives with support on the whole real line, whereas entropy-based tests are preferable for alternatives with support on the unit interval.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-06-17
2018
2018-01-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/112737
url https://hdl.handle.net/2117/112737
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institut d'Estadística de Catalunya
publisher.none.fl_str_mv Institut d'Estadística de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869423238163988480
score 15,300719

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