Externally studentized normal midrange distribution
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
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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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 |
_version_ |
1815439361674575872 |