Some generalized Burr XII distributions with applications to income and lifetime data

Detalhes bibliográficos
Autor(a) principal: GUERRA, Renata Rojas
Data de Publicação: 2017
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
dARK ID: ark:/64986/001300000cq08
Texto Completo: https://repositorio.ufpe.br/handle/123456789/25301
Resumo: The proposal of new continuous distributions by adding one or more shape parameter(s) to baseline models has attract researchers of many areas. Several generators have been studied in recent years that can be described as special cases of the transformed-transformer (T-X) method. The gamma generalized families (“gamma-G” for short), called Zografos-Balakrishnan-G (Zografos and Balakrishnan, 2009) and Ristic-Balakrishnan-G (Ristic and Balakrishnan, 2012), are important univariate distributions sub-families of the T-X generator. They are generated by gamma random variables. It was found that eighteen distributions have been studied as baselines in the gamma generalized families. Another known family of univariate distributions is generated by extending the Weibull model applied to the odds ratio G(x)=[1 – G(x)], called the Weibull-G (Bourguignon et al., 2014). It was found that seven distributions have been studied in the context of the Weibull-G family. The logistic-X (Tahir et al., 2016a) is also a sub-family on the T-X generator that was recently introduced in the literature. Considering this approach, we discuss in this thesis the gamma-G, logistic-X and Weibull-G families by taking the Burr XII distribution as baseline. We present density expansions, quantile functions, ordinary and incomplete moments, generating functions, estimation of the model parameters by maximum likelihood and provide applications to income and lifetime real data sets for the proposed distributions. We show that the new distributions yield good adjustments for the considered data sets and that they can be used effectively to obtain better fits than other classical models and Burr XII generated families.
id UFPE_c94e1d34f3baa54abcf0c7e2b1a5f0fb
oai_identifier_str oai:repositorio.ufpe.br:123456789/25301
network_acronym_str UFPE
network_name_str Repositório Institucional da UFPE
repository_id_str 2221
spelling GUERRA, Renata Rojashttp://lattes.cnpq.br/3142871647774939http://lattes.cnpq.br/3268732497595112CORDEIRO, Gauss Moutinho2018-07-31T22:07:24Z2018-07-31T22:07:24Z2017-05-30https://repositorio.ufpe.br/handle/123456789/25301ark:/64986/001300000cq08The proposal of new continuous distributions by adding one or more shape parameter(s) to baseline models has attract researchers of many areas. Several generators have been studied in recent years that can be described as special cases of the transformed-transformer (T-X) method. The gamma generalized families (“gamma-G” for short), called Zografos-Balakrishnan-G (Zografos and Balakrishnan, 2009) and Ristic-Balakrishnan-G (Ristic and Balakrishnan, 2012), are important univariate distributions sub-families of the T-X generator. They are generated by gamma random variables. It was found that eighteen distributions have been studied as baselines in the gamma generalized families. Another known family of univariate distributions is generated by extending the Weibull model applied to the odds ratio G(x)=[1 – G(x)], called the Weibull-G (Bourguignon et al., 2014). It was found that seven distributions have been studied in the context of the Weibull-G family. The logistic-X (Tahir et al., 2016a) is also a sub-family on the T-X generator that was recently introduced in the literature. Considering this approach, we discuss in this thesis the gamma-G, logistic-X and Weibull-G families by taking the Burr XII distribution as baseline. We present density expansions, quantile functions, ordinary and incomplete moments, generating functions, estimation of the model parameters by maximum likelihood and provide applications to income and lifetime real data sets for the proposed distributions. We show that the new distributions yield good adjustments for the considered data sets and that they can be used effectively to obtain better fits than other classical models and Burr XII generated families.A ideia de obter novas distribuições contínuas adicionando um ou mais parâmetros a uma distribuição de base (baseline) tem atraído pesquisadores de diversas áreas. Muitos geradores de distribuições têm sido estudados nos últimos anos. Diversos deles podem ser descritos como casos especias da família de geradores transformed-transformer (T-X). Neste contexto, as famílias gama generalizadas (gamma-G), denominadas Zografos-Balakrishnan-G (Zografos and Balakrishnan, 2009) e Ristic-Balakrishnan-G (Ristic and Balakrishnan, 2012), são importantes subfamílias de distribuições univariadas do gerador T-X, as quais são obtidas a partir de variáveis aleatórias com distribuição gama. Na literatura foi possível encontrar dezoito distribuições que foram estudadas como baselines nestas famílias. Outra conhecida sub-família do gerador T-X é gerada a partir da distribuição de Weibull aplicada à razão de chances G(x)=[1 – G(x)], denominada família Weibull-G. Na literatura foi possível encontrar sete distribuições estudadas como baselines na família Weibull-G (Bourguignon et al., 2014). A família logistic-X (Tahir et al., 2016a) é também uma sub-família do gerador T-X recentemente introduzida na literatura. Nesta tese serão discutidas as famílias gamma-G, logistic-X e Weibull-G, considerando a distribuição Burr XII como baseline. Serão apresentadas expansões para a função de densidade, a função quantílica, momentos ordinários incompletos, funções geradoras de momentos e estimação por máxima verossimilhança. Também são realizadas aplicações das novas distribuições a conjuntos de dados reais de renda e de análise de sobrevivência. As distribuições propostas obtiveram ajustes adequados para as bases de dados consideradas, podendo ser utilizadas como alternativas efetivas a outros modelos clássicos e, também, a outras generalizações da distribuição Burr XII.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEstatística aplicadaProbabilidadeSome generalized Burr XII distributions with applications to income and lifetime dataSome generalized BXII distributions with applications to income and lifetime datainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Renata Rojas Guerra.pdf.jpgTESE Renata Rojas Guerra.pdf.jpgGenerated Thumbnailimage/jpeg1227https://repositorio.ufpe.br/bitstream/123456789/25301/5/TESE%20Renata%20Rojas%20Guerra.pdf.jpg0d207850dd2a5cccc3f941a7defdb844MD55ORIGINALTESE Renata Rojas Guerra.pdfTESE Renata Rojas Guerra.pdfapplication/pdf1885947https://repositorio.ufpe.br/bitstream/123456789/25301/1/TESE%20Renata%20Rojas%20Guerra.pdff3735652f8d33d6ded71b89129232867MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/25301/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82311https://repositorio.ufpe.br/bitstream/123456789/25301/3/license.txt4b8a02c7f2818eaf00dcf2260dd5eb08MD53TEXTTESE Renata Rojas Guerra.pdf.txtTESE Renata Rojas Guerra.pdf.txtExtracted texttext/plain181095https://repositorio.ufpe.br/bitstream/123456789/25301/4/TESE%20Renata%20Rojas%20Guerra.pdf.txta46e32c2b3a5e6113e39af45f156a4b5MD54123456789/253012019-10-26 01:15:21.742oai:repositorio.ufpe.br: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Repositório InstitucionalPUBhttps://repositorio.ufpe.br/oai/requestattena@ufpe.bropendoar:22212019-10-26T04:15:21Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)false
dc.title.pt_BR.fl_str_mv Some generalized Burr XII distributions with applications to income and lifetime data
dc.title.alternative.pt_BR.fl_str_mv Some generalized BXII distributions with applications to income and lifetime data
title Some generalized Burr XII distributions with applications to income and lifetime data
spellingShingle Some generalized Burr XII distributions with applications to income and lifetime data
GUERRA, Renata Rojas
Estatística aplicada
Probabilidade
title_short Some generalized Burr XII distributions with applications to income and lifetime data
title_full Some generalized Burr XII distributions with applications to income and lifetime data
title_fullStr Some generalized Burr XII distributions with applications to income and lifetime data
title_full_unstemmed Some generalized Burr XII distributions with applications to income and lifetime data
title_sort Some generalized Burr XII distributions with applications to income and lifetime data
author GUERRA, Renata Rojas
author_facet GUERRA, Renata Rojas
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/3142871647774939
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/3268732497595112
dc.contributor.author.fl_str_mv GUERRA, Renata Rojas
dc.contributor.advisor1.fl_str_mv CORDEIRO, Gauss Moutinho
contributor_str_mv CORDEIRO, Gauss Moutinho
dc.subject.por.fl_str_mv Estatística aplicada
Probabilidade
topic Estatística aplicada
Probabilidade
description The proposal of new continuous distributions by adding one or more shape parameter(s) to baseline models has attract researchers of many areas. Several generators have been studied in recent years that can be described as special cases of the transformed-transformer (T-X) method. The gamma generalized families (“gamma-G” for short), called Zografos-Balakrishnan-G (Zografos and Balakrishnan, 2009) and Ristic-Balakrishnan-G (Ristic and Balakrishnan, 2012), are important univariate distributions sub-families of the T-X generator. They are generated by gamma random variables. It was found that eighteen distributions have been studied as baselines in the gamma generalized families. Another known family of univariate distributions is generated by extending the Weibull model applied to the odds ratio G(x)=[1 – G(x)], called the Weibull-G (Bourguignon et al., 2014). It was found that seven distributions have been studied in the context of the Weibull-G family. The logistic-X (Tahir et al., 2016a) is also a sub-family on the T-X generator that was recently introduced in the literature. Considering this approach, we discuss in this thesis the gamma-G, logistic-X and Weibull-G families by taking the Burr XII distribution as baseline. We present density expansions, quantile functions, ordinary and incomplete moments, generating functions, estimation of the model parameters by maximum likelihood and provide applications to income and lifetime real data sets for the proposed distributions. We show that the new distributions yield good adjustments for the considered data sets and that they can be used effectively to obtain better fits than other classical models and Burr XII generated families.
publishDate 2017
dc.date.issued.fl_str_mv 2017-05-30
dc.date.accessioned.fl_str_mv 2018-07-31T22:07:24Z
dc.date.available.fl_str_mv 2018-07-31T22:07:24Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/25301
dc.identifier.dark.fl_str_mv ark:/64986/001300000cq08
url https://repositorio.ufpe.br/handle/123456789/25301
identifier_str_mv ark:/64986/001300000cq08
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Estatistica
dc.publisher.initials.fl_str_mv UFPE
dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFPE
instname:Universidade Federal de Pernambuco (UFPE)
instacron:UFPE
instname_str Universidade Federal de Pernambuco (UFPE)
instacron_str UFPE
institution UFPE
reponame_str Repositório Institucional da UFPE
collection Repositório Institucional da UFPE
bitstream.url.fl_str_mv https://repositorio.ufpe.br/bitstream/123456789/25301/5/TESE%20Renata%20Rojas%20Guerra.pdf.jpg
https://repositorio.ufpe.br/bitstream/123456789/25301/1/TESE%20Renata%20Rojas%20Guerra.pdf
https://repositorio.ufpe.br/bitstream/123456789/25301/2/license_rdf
https://repositorio.ufpe.br/bitstream/123456789/25301/3/license.txt
https://repositorio.ufpe.br/bitstream/123456789/25301/4/TESE%20Renata%20Rojas%20Guerra.pdf.txt
bitstream.checksum.fl_str_mv 0d207850dd2a5cccc3f941a7defdb844
f3735652f8d33d6ded71b89129232867
e39d27027a6cc9cb039ad269a5db8e34
4b8a02c7f2818eaf00dcf2260dd5eb08
a46e32c2b3a5e6113e39af45f156a4b5
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)
repository.mail.fl_str_mv attena@ufpe.br
_version_ 1815172791056465920