Some generalized Burr XII distributions with applications to income and lifetime data
Autor(a) principal: | |
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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. |
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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; 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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 |
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Universidade Federal de Pernambuco (UFPE) |
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UFPE |
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UFPE |
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Repositório Institucional da UFPE |
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Repositório Institucional da UFPE |
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