Some extended Alpha models: properties and applications
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/24965 |
Resumo: | Generalizing distributions provide some advantages, allowing us to define new families, to extend well-known distributions and provide great flexibility in modeling real data, which can be applied in several fields. The Alpha distribution was studied for the first time to analyze tool wear problems by Katsev (1968) and Wager and Barash (1971). Salvia (1985) provided its characterization. In this thesis, we discuss the Alpha distribution, we present a simulation study to verify the performance of its maximum likelihood estimators and four real data sets are used to evaluate the Alpha model when compared to some distributions well-known in literature. Furthermore, we developed new distributions considering this model as the baseline distribution applied to Exponentiated class (Gompertz, 1825; Verhulst, 1838, 1845, 1847) and Kumaraswamy class, proposed by Cordeiro and de Castro (2011). We also propose a new family of distributions, called Exponentiated Generalized Exponentiated-Generated (EG-Exp-G), which is an extension of the exponentiated generalized class proposed by Cordeiro et al. (2013). Some new distributions are proposed as submodels of this family, including the EG-Exp-Alpha distribution. We study some mathematical properties, such as quantile function, moments, moment generating function, mean deviations and order statistics. In addition, we use the maximum likelihood method to estimate the parameters of the proposed models. We perform Monte Carlo simulation studies to analyze the asymptotic properties of the maximum likelihood estimators and we illustrate the flexibility of the new models through applications to real data set in order to show their competitiveness compared to well-known distributions in the literature. |
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RODRIGUES, Heloisa de Melohttp://lattes.cnpq.br/4856660040980107http://lattes.cnpq.br/3295616000667012CYSNEIROS, Audrey Helen Mariz de Aquino2018-07-03T20:47:05Z2018-07-03T20:47:05Z2017-02-20https://repositorio.ufpe.br/handle/123456789/24965Generalizing distributions provide some advantages, allowing us to define new families, to extend well-known distributions and provide great flexibility in modeling real data, which can be applied in several fields. The Alpha distribution was studied for the first time to analyze tool wear problems by Katsev (1968) and Wager and Barash (1971). Salvia (1985) provided its characterization. In this thesis, we discuss the Alpha distribution, we present a simulation study to verify the performance of its maximum likelihood estimators and four real data sets are used to evaluate the Alpha model when compared to some distributions well-known in literature. Furthermore, we developed new distributions considering this model as the baseline distribution applied to Exponentiated class (Gompertz, 1825; Verhulst, 1838, 1845, 1847) and Kumaraswamy class, proposed by Cordeiro and de Castro (2011). We also propose a new family of distributions, called Exponentiated Generalized Exponentiated-Generated (EG-Exp-G), which is an extension of the exponentiated generalized class proposed by Cordeiro et al. (2013). Some new distributions are proposed as submodels of this family, including the EG-Exp-Alpha distribution. We study some mathematical properties, such as quantile function, moments, moment generating function, mean deviations and order statistics. In addition, we use the maximum likelihood method to estimate the parameters of the proposed models. We perform Monte Carlo simulation studies to analyze the asymptotic properties of the maximum likelihood estimators and we illustrate the flexibility of the new models through applications to real data set in order to show their competitiveness compared to well-known distributions in the literature.A generalização de distribuições oferece algumas vantagens, permitindo-nos definir novas famílias, estender distribuições conhecidas e proporcionar grande flexibilidade na modelagem de dados reais, que podem ser aplicados em vários campos. A distribuição Alpha foi estudada inicialmente para analisar problemas de desgaste de ferramentas por Katsev (1968) e Wager e Barash (1971). Salvia (1985) forneceu algumas características desta distribuição. Nesta tese, discutimos a distribuição Alpha, apresentamos um estudo de simulação para verificar a performance dos seus estimadores de máxima verssimilhança e quatro conjuntos de dados reais são utilizados para avaliar o modelo Alpha em relação à algumas distribuições de probabilidade já conhecidas na literatura. Além disso, desenvolvemos novas distribuições considerando tal modelo como distribuição de base aplicada aos geradores da Exponencializada (Gompertz, 1825; Verhulst, 1838, 1845, 1847) e da Kumaraswamy, proposta por Cordeiro e de Castro (2011). Propomos ainda uma nova família de distribuições, chamada exponencializada generalizada exponencializada (EG-Exp-G), que é uma extensão da classe exponencializada generalizada proposta por Cordeiro et al. (2013). Apresentamos alguns casos especiais deste novo gerador, entre eles a distribuição EG-Exp-Alpha. Desenvolvemos algumas propriedades matemáticas, a saber: desvios médios, estatísticas de ordem, função geratriz de momentos, função quantílica e momentos. Além disso, utilizamos o método de máxima verossimilhança para estimação dos parâmetros dos modelos propostos. Realizamos estudos de simulação de Monte Carlo visando analisar as propriedades assintóticas dos estimadores de máxima verossimilhança e ilustramos a #exibilidade dos novos modelos por meio de aplicações a dados reais a fim de mostrar a competitividade deles comparados às distribuições de probabilidade já conhecidas na literatura.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/openAccessAnálise de regressãoMáxima verossimilhançaSome extended Alpha models: properties and applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Heloisa de Melo Rodrigues.pdf.jpgTESE Heloisa de Melo Rodrigues.pdf.jpgGenerated Thumbnailimage/jpeg1154https://repositorio.ufpe.br/bitstream/123456789/24965/5/TESE%20Heloisa%20de%20Melo%20Rodrigues.pdf.jpg0d9dabd99ef0ff964b0d7dec4a64e305MD55ORIGINALTESE Heloisa de Melo Rodrigues.pdfTESE Heloisa de Melo Rodrigues.pdfapplication/pdf1213024https://repositorio.ufpe.br/bitstream/123456789/24965/1/TESE%20Heloisa%20de%20Melo%20Rodrigues.pdf1049fe1e9beafa94b63a5bd024324972MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Some extended Alpha models: properties and applications |
title |
Some extended Alpha models: properties and applications |
spellingShingle |
Some extended Alpha models: properties and applications RODRIGUES, Heloisa de Melo Análise de regressão Máxima verossimilhança |
title_short |
Some extended Alpha models: properties and applications |
title_full |
Some extended Alpha models: properties and applications |
title_fullStr |
Some extended Alpha models: properties and applications |
title_full_unstemmed |
Some extended Alpha models: properties and applications |
title_sort |
Some extended Alpha models: properties and applications |
author |
RODRIGUES, Heloisa de Melo |
author_facet |
RODRIGUES, Heloisa de Melo |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/4856660040980107 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/3295616000667012 |
dc.contributor.author.fl_str_mv |
RODRIGUES, Heloisa de Melo |
dc.contributor.advisor1.fl_str_mv |
CYSNEIROS, Audrey Helen Mariz de Aquino |
contributor_str_mv |
CYSNEIROS, Audrey Helen Mariz de Aquino |
dc.subject.por.fl_str_mv |
Análise de regressão Máxima verossimilhança |
topic |
Análise de regressão Máxima verossimilhança |
description |
Generalizing distributions provide some advantages, allowing us to define new families, to extend well-known distributions and provide great flexibility in modeling real data, which can be applied in several fields. The Alpha distribution was studied for the first time to analyze tool wear problems by Katsev (1968) and Wager and Barash (1971). Salvia (1985) provided its characterization. In this thesis, we discuss the Alpha distribution, we present a simulation study to verify the performance of its maximum likelihood estimators and four real data sets are used to evaluate the Alpha model when compared to some distributions well-known in literature. Furthermore, we developed new distributions considering this model as the baseline distribution applied to Exponentiated class (Gompertz, 1825; Verhulst, 1838, 1845, 1847) and Kumaraswamy class, proposed by Cordeiro and de Castro (2011). We also propose a new family of distributions, called Exponentiated Generalized Exponentiated-Generated (EG-Exp-G), which is an extension of the exponentiated generalized class proposed by Cordeiro et al. (2013). Some new distributions are proposed as submodels of this family, including the EG-Exp-Alpha distribution. We study some mathematical properties, such as quantile function, moments, moment generating function, mean deviations and order statistics. In addition, we use the maximum likelihood method to estimate the parameters of the proposed models. We perform Monte Carlo simulation studies to analyze the asymptotic properties of the maximum likelihood estimators and we illustrate the flexibility of the new models through applications to real data set in order to show their competitiveness compared to well-known distributions in the literature. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-02-20 |
dc.date.accessioned.fl_str_mv |
2018-07-03T20:47:05Z |
dc.date.available.fl_str_mv |
2018-07-03T20:47:05Z |
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/123456789/24965 |
url |
https://repositorio.ufpe.br/handle/123456789/24965 |
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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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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