Externally studentized normal midrange distribution

Detalhes bibliográficos
Autor(a) principal: Batista, Ben Dêivide de Oliveira
Data de Publicação: 2017
Outros Autores: Ferreira, Daniel Furtado, Chaves, Lucas Monteiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFLA
Texto Completo: http://repositorio.ufla.br/jspui/handle/1/29962
Resumo: The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.
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spelling Externally studentized normal midrange distributionDistribuição da midrange estudentizada externamenteDistribution functionDensity functionGauss-Legendre quadratureNewton-Raphson methodSoftware RFunção de distribuiçãoFunção densidadeQuadratura Gauss-LegendreMétodo Newton-RaphsonAlgoritmoThe distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.A distribuição da midrange estudentizada externamente foi criada com base nos procedimentos de estudentização de Student e foi inspirada na distribuição da amplitude estudentizada externamente. O amplo uso da amplitude estudentizada externamente em comparações múltiplas também foi uma das motivações para desenvolver esta nova distribuição. Neste trabalho objetivou-se derivar expressões analíticas da distribuição da midrange estudentizada externamente, obtendo a função de distribuição, função densidade de probabilidade, função quantil e geradores de números aleatórios. Essa é uma nova distribuição que os não há relatos na literatura especializada. Um segundo objetivo foi construir um pacote R para obter numericamente as funções mencionadas e torná-las disponíveis para a comunidade científica. Os algoritmos foram propostos e implementados usando os métodos de quadratura Gauss-Legendre e Newton-Raphson no software R, resultando no pacote SMR, disponível para baixar na página do CRAN. As rotinas implementadas apresentaram alta acurácia, sendo verificadas usando simulação Monte Carlo e pela comparação com diferentes pontos de quadratura. Quanto a precisão para se obter os quantis da distribuição da midrange estudentizada externamente para 1 grau de liberdade ou percentis próximo de 100%, é sugerido utilizar mais do que 64 pontos de quadratura.Universidade Federal de Lavras2018-08-13T18:42:26Z2018-08-13T18:42:26Z2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBATISTA, B. D. de O.; FERREIRA, D. F.; CHAVES L. M. Externally studentized normal midrange distribution. Ciência e Agrotecnologia, Lavras, v. 41, n. 4, p. 378-389, July/Aug. 2017.http://repositorio.ufla.br/jspui/handle/1/29962Ciência e Agrotecnologiareponame:Repositório Institucional da UFLAinstname:Universidade Federal de Lavras (UFLA)instacron:UFLAAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessBatista, Ben Dêivide de OliveiraFerreira, Daniel FurtadoChaves, Lucas Monteiroeng2023-05-26T19:43:46Zoai:localhost:1/29962Repositório InstitucionalPUBhttp://repositorio.ufla.br/oai/requestnivaldo@ufla.br || repositorio.biblioteca@ufla.bropendoar:2023-05-26T19:43:46Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA)false
dc.title.none.fl_str_mv Externally studentized normal midrange distribution
Distribuição da midrange estudentizada externamente
title Externally studentized normal midrange distribution
spellingShingle Externally studentized normal midrange distribution
Batista, Ben Dêivide de Oliveira
Distribution function
Density function
Gauss-Legendre quadrature
Newton-Raphson method
Software R
Função de distribuição
Função densidade
Quadratura Gauss-Legendre
Método Newton-Raphson
Algoritmo
title_short Externally studentized normal midrange distribution
title_full Externally studentized normal midrange distribution
title_fullStr Externally studentized normal midrange distribution
title_full_unstemmed Externally studentized normal midrange distribution
title_sort Externally studentized normal midrange distribution
author Batista, Ben Dêivide de Oliveira
author_facet Batista, Ben Dêivide de Oliveira
Ferreira, Daniel Furtado
Chaves, Lucas Monteiro
author_role author
author2 Ferreira, Daniel Furtado
Chaves, Lucas Monteiro
author2_role author
author
dc.contributor.author.fl_str_mv Batista, Ben Dêivide de Oliveira
Ferreira, Daniel Furtado
Chaves, Lucas Monteiro
dc.subject.por.fl_str_mv Distribution function
Density function
Gauss-Legendre quadrature
Newton-Raphson method
Software R
Função de distribuição
Função densidade
Quadratura Gauss-Legendre
Método Newton-Raphson
Algoritmo
topic Distribution function
Density function
Gauss-Legendre quadrature
Newton-Raphson method
Software R
Função de distribuição
Função densidade
Quadratura Gauss-Legendre
Método Newton-Raphson
Algoritmo
description The distribution of externally studentized midrange was created based on the original studentization procedures of Student and was inspired in the distribution of the externally studentized range. The large use of the externally studentized range in multiple comparisons was also a motivation for developing this new distribution. This work aimed to derive analytic equations to distribution of the externally studentized midrange, obtaining the cumulative distribution, probability density and quantile functions and generating random values. This is a new distribution that the authors could not find any report in the literature. A second objective was to build an R package for obtaining numerically the probability density, cumulative distribution and quantile functions and make it available to the scientific community. The algorithms were proposed and implemented using Gauss-Legendre quadrature and the Newton-Raphson method in R software, resulting in the SMR package, available for download in the CRAN site. The implemented routines showed high accuracy proved by using Monte Carlo simulations and by comparing results with different number of quadrature points. Regarding to the precision to obtain the quantiles for cases where the degrees of freedom are close to 1 and the percentiles are close to 100%, it is recommended to use more than 64 quadrature points.
publishDate 2017
dc.date.none.fl_str_mv 2017
2018-08-13T18:42:26Z
2018-08-13T18:42:26Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv BATISTA, B. D. de O.; FERREIRA, D. F.; CHAVES L. M. Externally studentized normal midrange distribution. Ciência e Agrotecnologia, Lavras, v. 41, n. 4, p. 378-389, July/Aug. 2017.
http://repositorio.ufla.br/jspui/handle/1/29962
identifier_str_mv BATISTA, B. D. de O.; FERREIRA, D. F.; CHAVES L. M. Externally studentized normal midrange distribution. Ciência e Agrotecnologia, Lavras, v. 41, n. 4, p. 378-389, July/Aug. 2017.
url http://repositorio.ufla.br/jspui/handle/1/29962
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Lavras
publisher.none.fl_str_mv Universidade Federal de Lavras
dc.source.none.fl_str_mv Ciência e Agrotecnologia
reponame:Repositório Institucional da UFLA
instname:Universidade Federal de Lavras (UFLA)
instacron:UFLA
instname_str Universidade Federal de Lavras (UFLA)
instacron_str UFLA
institution UFLA
reponame_str Repositório Institucional da UFLA
collection Repositório Institucional da UFLA
repository.name.fl_str_mv Repositório Institucional da UFLA - Universidade Federal de Lavras (UFLA)
repository.mail.fl_str_mv nivaldo@ufla.br || repositorio.biblioteca@ufla.br
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