Some new families of continuos distributions
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/18862 |
Resumo: | The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean the life itself of a person, the operating time of equipment until its failure, the time of survival of a patient with a severe disease from the diagnosis, the duration of a social event as a marriage, among other meanings. The time of life or survival time is a positive continuous random variable, which can have constant, monotonic increasing, monotonic decreasing or non-monotonic (for example, in the form of a U) hazard function. In the last decades, several families of probabilistic models have been proposed. These models can be constructed based on some transformation of a parent distribution, commonly already known in the literature. A given linear combination or mixture of G models usually defines a class of probabilistic models having G as a special case. This thesis is composed of independent chapters. The first and last chapters are short chapters that include the introduction and conclusions of the study developed. Two families of distributions, namely the exponentiated logarithmic generated (ELG) class and the geometric Nadarajah-Haghighi (NHG) class are studied. The last one is a composition of the Nadarajah-Haghighi and geometric distributions. Further, we develop a statistical library for the R programming language called the AdequacyModel. This is an improvement of the package that was available on CRAN (Comprehensive R Archive Network) and it is currently in version 2.0.0. The two main functions of the library are the goodness.fit and pso functions. The first function allows to obtain the maximum likelihood estimates (MLEs) of the model parameters and some goodness-of-fit of the fitted probabilistic models. It is possible to choose the method of optimization for maximizing the log-likelihood function. The second function presents the method meta-heuristics global search known as particle swarm optimization (PSO) proposed by Eberhart and Kennedy (1995). Such methodology can be used for obtaining the MLEs necessary for the calculation of some measures of adequacy of the probabilistic models. |
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MARINHO, Pedro Rafael Dinizhttp://lattes.cnpq.br/7185368598935272http://lattes.cnpq.br/3268732497595112CORDEIRO, Gauss Moutinho2017-05-23T12:23:58Z2017-05-23T12:23:58Z2016-06-27https://repositorio.ufpe.br/handle/123456789/18862The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean the life itself of a person, the operating time of equipment until its failure, the time of survival of a patient with a severe disease from the diagnosis, the duration of a social event as a marriage, among other meanings. The time of life or survival time is a positive continuous random variable, which can have constant, monotonic increasing, monotonic decreasing or non-monotonic (for example, in the form of a U) hazard function. In the last decades, several families of probabilistic models have been proposed. These models can be constructed based on some transformation of a parent distribution, commonly already known in the literature. A given linear combination or mixture of G models usually defines a class of probabilistic models having G as a special case. This thesis is composed of independent chapters. The first and last chapters are short chapters that include the introduction and conclusions of the study developed. Two families of distributions, namely the exponentiated logarithmic generated (ELG) class and the geometric Nadarajah-Haghighi (NHG) class are studied. The last one is a composition of the Nadarajah-Haghighi and geometric distributions. Further, we develop a statistical library for the R programming language called the AdequacyModel. This is an improvement of the package that was available on CRAN (Comprehensive R Archive Network) and it is currently in version 2.0.0. The two main functions of the library are the goodness.fit and pso functions. The first function allows to obtain the maximum likelihood estimates (MLEs) of the model parameters and some goodness-of-fit of the fitted probabilistic models. It is possible to choose the method of optimization for maximizing the log-likelihood function. The second function presents the method meta-heuristics global search known as particle swarm optimization (PSO) proposed by Eberhart and Kennedy (1995). Such methodology can be used for obtaining the MLEs necessary for the calculation of some measures of adequacy of the probabilistic models.FACEPEA área de análise de sobrevivência é importante na Estatística e é comumente aplicada às ciências biológicas, engenharias, ciências sociais, entre outras. Tipicamente, o tempo de vida ou falha pode ter diferentes interpretações dependendo da área de aplicação. Por exemplo, o tempo de vida pode significar a própria vida de uma pessoa, o tempo de funcionamento de um equipamento até sua falha, o tempo de sobrevivência de um paciente com uma doença grave desde o diagnóstico, a duração de um evento social como um casamento, entre outros significados. O tempo de vida é uma variável aleatória não negativa, que pode ter a função de risco na forma constante, monótona crescente, monótona decrescente ou não monótona (por exemplo, em forma de U). Nas últimas décadas, várias famílias de modelos probabilísticos têm sido propostas. Esses modelos podem ser construídos com base em alguma transformação de uma distribuição padrão, geralmente já conhecida na literatura. Uma dada combinação linear ou mistura de modelos G normalmente define uma classe de modelos probabilísticos tendo G como caso especial. Esta tese é composta de capítulos independentes. O primeiro e último são curtos capítulos que incluem a introdução e as conclusões do estudo desenvolvido. Duas famílias de distribuições, denominadas de classe “exponentiated logarithmic generated” (ELG) e a classe “geometric Nadarajah-Haghighi” (NHG) s˜ao estudadas. A ´ultima ´e uma composi¸c˜ao das distribuições de Nadarajah-Haghighi e geométrica. Além disso, desenvolvemos uma biblioteca estatística para a linguagem de programação R chamada AdequacyModel. Esta é uma melhoria do pacote que foi disponibilizado no CRAN (Comprehensive R Archive Network) e está atualmente na versão 2.0.0. As duas principais funções da biblioteca são as funções goodness.fit e pso. A primeira função permite obter as estimativas de máxima verossimilhança (EMVs) dos parâmetros de um modelo e algumas medidas de bondade de ajuste dos modelos probabilísticos ajustados. E possível escolher o método de otimização para maximizar a função de log-verossimilhan¸ca. A segunda função apresenta o método meta-heurístico de busca global conhecido como Particle Swarm Optimization (PSO) proposto por Eberhart e Kennedy (1995). Algumas metodologias podem ser utilizadas para obtenção das EMVs necessárias para o cálculo de algumas medidas de adequação dos modelos probablísticos ajustados.porUniversidade 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/openAccessAdequacy ModelDistribuiçãomistura linearPSOAdequacy Model packageDistributionLinear mixturePSOSome new families of continuos distributionsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILSOME NEW FAMILIES OF CONTINUOUS DISTRIBUTIONS.pdf.jpgSOME NEW FAMILIES OF CONTINUOUS DISTRIBUTIONS.pdf.jpgGenerated Thumbnailimage/jpeg1221https://repositorio.ufpe.br/bitstream/123456789/18862/5/SOME%20NEW%20FAMILIES%20OF%20CONTINUOUS%20DISTRIBUTIONS.pdf.jpgd3793ef76fa4ea5cb744574fe1c0184dMD55ORIGINALSOME NEW FAMILIES OF CONTINUOUS DISTRIBUTIONS.pdfSOME NEW FAMILIES OF CONTINUOUS DISTRIBUTIONS.pdfapplication/pdf5612905https://repositorio.ufpe.br/bitstream/123456789/18862/1/SOME%20NEW%20FAMILIES%20OF%20CONTINUOUS%20DISTRIBUTIONS.pdf3fd32464f68606705a4b23070897a8e2MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Some new families of continuos distributions |
title |
Some new families of continuos distributions |
spellingShingle |
Some new families of continuos distributions MARINHO, Pedro Rafael Diniz Adequacy Model Distribuição mistura linear PSO Adequacy Model package Distribution Linear mixture PSO |
title_short |
Some new families of continuos distributions |
title_full |
Some new families of continuos distributions |
title_fullStr |
Some new families of continuos distributions |
title_full_unstemmed |
Some new families of continuos distributions |
title_sort |
Some new families of continuos distributions |
author |
MARINHO, Pedro Rafael Diniz |
author_facet |
MARINHO, Pedro Rafael Diniz |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/7185368598935272 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/3268732497595112 |
dc.contributor.author.fl_str_mv |
MARINHO, Pedro Rafael Diniz |
dc.contributor.advisor1.fl_str_mv |
CORDEIRO, Gauss Moutinho |
contributor_str_mv |
CORDEIRO, Gauss Moutinho |
dc.subject.por.fl_str_mv |
Adequacy Model Distribuição mistura linear PSO Adequacy Model package Distribution Linear mixture PSO |
topic |
Adequacy Model Distribuição mistura linear PSO Adequacy Model package Distribution Linear mixture PSO |
description |
The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean the life itself of a person, the operating time of equipment until its failure, the time of survival of a patient with a severe disease from the diagnosis, the duration of a social event as a marriage, among other meanings. The time of life or survival time is a positive continuous random variable, which can have constant, monotonic increasing, monotonic decreasing or non-monotonic (for example, in the form of a U) hazard function. In the last decades, several families of probabilistic models have been proposed. These models can be constructed based on some transformation of a parent distribution, commonly already known in the literature. A given linear combination or mixture of G models usually defines a class of probabilistic models having G as a special case. This thesis is composed of independent chapters. The first and last chapters are short chapters that include the introduction and conclusions of the study developed. Two families of distributions, namely the exponentiated logarithmic generated (ELG) class and the geometric Nadarajah-Haghighi (NHG) class are studied. The last one is a composition of the Nadarajah-Haghighi and geometric distributions. Further, we develop a statistical library for the R programming language called the AdequacyModel. This is an improvement of the package that was available on CRAN (Comprehensive R Archive Network) and it is currently in version 2.0.0. The two main functions of the library are the goodness.fit and pso functions. The first function allows to obtain the maximum likelihood estimates (MLEs) of the model parameters and some goodness-of-fit of the fitted probabilistic models. It is possible to choose the method of optimization for maximizing the log-likelihood function. The second function presents the method meta-heuristics global search known as particle swarm optimization (PSO) proposed by Eberhart and Kennedy (1995). Such methodology can be used for obtaining the MLEs necessary for the calculation of some measures of adequacy of the probabilistic models. |
publishDate |
2016 |
dc.date.issued.fl_str_mv |
2016-06-27 |
dc.date.accessioned.fl_str_mv |
2017-05-23T12:23:58Z |
dc.date.available.fl_str_mv |
2017-05-23T12:23:58Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
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doctoralThesis |
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publishedVersion |
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https://repositorio.ufpe.br/handle/123456789/18862 |
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https://repositorio.ufpe.br/handle/123456789/18862 |
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por |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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Programa de Pos Graduacao em Estatistica |
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UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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