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: Ciência e Agrotecnologia (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542017000400378
Resumo: ABSTRACT 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 distributionDistribution functiondensity functionGauss-Legendre quadratureNewton-Raphson methodR.ABSTRACT 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.Editora da UFLA2017-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542017000400378Ciência e Agrotecnologia v.41 n.4 2017reponame:Ciência e Agrotecnologia (Online)instname:Universidade Federal de Lavras (UFLA)instacron:UFLA10.1590/1413-70542017414047716info:eu-repo/semantics/openAccessBatista,Ben Dêivide de OliveiraFerreira,Daniel FurtadoChaves,Lucas Monteiroeng2017-10-11T00:00:00Zoai:scielo:S1413-70542017000400378Revistahttp://www.scielo.br/cagroPUBhttps://old.scielo.br/oai/scielo-oai.php||renpaiva@dbi.ufla.br|| editora@editora.ufla.br1981-18291413-7054opendoar:2022-11-22T16:31:32.038493Ciência e Agrotecnologia (Online) - Universidade Federal de Lavras (UFLA)true
dc.title.none.fl_str_mv Externally studentized normal midrange distribution
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
R.
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
R.
topic Distribution function
density function
Gauss-Legendre quadrature
Newton-Raphson method
R.
description ABSTRACT 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 2017-07-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542017000400378
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1413-70542017000400378
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/1413-70542017414047716
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Editora da UFLA
publisher.none.fl_str_mv Editora da UFLA
dc.source.none.fl_str_mv Ciência e Agrotecnologia v.41 n.4 2017
reponame:Ciência e Agrotecnologia (Online)
instname:Universidade Federal de Lavras (UFLA)
instacron:UFLA
instname_str Universidade Federal de Lavras (UFLA)
instacron_str UFLA
institution UFLA
reponame_str Ciência e Agrotecnologia (Online)
collection Ciência e Agrotecnologia (Online)
repository.name.fl_str_mv Ciência e Agrotecnologia (Online) - Universidade Federal de Lavras (UFLA)
repository.mail.fl_str_mv ||renpaiva@dbi.ufla.br|| editora@editora.ufla.br
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