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: | 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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Ciência e Agrotecnologia (Online) |
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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 |
_version_ |
1799874970651721728 |