Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://hdl.handle.net/11449/192924 |
Resumo: | This work presents a study of probabilistic modeling, with applications to survival analysis, based on a probabilistic model called Exponential Geometric (EG), which o ers great exibility for the statistical estimation of its parameters based on samples of life time data complete and censored. In this study, the concepts of estimators and lifetime data are explored under random censorship in two cases of extensions of the EG model: the Extended Geometric Exponential (EEG) and the Generalized Extreme Geometric Exponential (GE2). The work still considers, exclusively for the EEG model, the approach of the presence of covariates indexed in the rate parameter as a second source of variation to add even more exibility to the model, as well as, exclusively for the GE2 model, a analysis of the convergence, hitherto ignored, it is proposed for its moments. The statistical inference approach is performed for these extensions in order to expose (in the classical context) their maximum likelihood estimators and asymptotic con dence intervals, and (in the bayesian context) their a priori and a posteriori distributions, both cases to estimate their parameters under random censorship, and covariates in the case of EEG. In this work, bayesian estimators are developed with the assumptions that the prioris are vague, follow a Gamma distribution and are independent between the unknown parameters. The results of this work are regarded from a detailed study of statistical simulation applied to compare the estimation procedures approached under the pretext of evaluating these estimators based on the 95% coverage probability, mean square error, mean bias and the mean interval amplitude. At the end of each extension's approach, an application with real data is also presented to highlight the reach and particularities of the extended model addressed. |
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Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censoredInferência bayesiana e clássica para extensões da distribuição Exponencial Geométrica com aplicações em análise de sobrevivência sob dados covariados e aleatoriamente censuradosCensored and covariate dataMaximum likelihood and bayesian estimationExtensions for Exponential Geometric distributionStatistical simulationDados censurados e covariadosEstimação de máxima verossimilhança e bayesianoExtensões para a distribuição Exponencial GeométricaSimulação estatísticaThis work presents a study of probabilistic modeling, with applications to survival analysis, based on a probabilistic model called Exponential Geometric (EG), which o ers great exibility for the statistical estimation of its parameters based on samples of life time data complete and censored. In this study, the concepts of estimators and lifetime data are explored under random censorship in two cases of extensions of the EG model: the Extended Geometric Exponential (EEG) and the Generalized Extreme Geometric Exponential (GE2). The work still considers, exclusively for the EEG model, the approach of the presence of covariates indexed in the rate parameter as a second source of variation to add even more exibility to the model, as well as, exclusively for the GE2 model, a analysis of the convergence, hitherto ignored, it is proposed for its moments. The statistical inference approach is performed for these extensions in order to expose (in the classical context) their maximum likelihood estimators and asymptotic con dence intervals, and (in the bayesian context) their a priori and a posteriori distributions, both cases to estimate their parameters under random censorship, and covariates in the case of EEG. In this work, bayesian estimators are developed with the assumptions that the prioris are vague, follow a Gamma distribution and are independent between the unknown parameters. The results of this work are regarded from a detailed study of statistical simulation applied to compare the estimation procedures approached under the pretext of evaluating these estimators based on the 95% coverage probability, mean square error, mean bias and the mean interval amplitude. At the end of each extension's approach, an application with real data is also presented to highlight the reach and particularities of the extended model addressed.Este trabalho apresenta um estudo de modelagem probabilística, com aplicações à análise de sobrevivência, fundamentado em um modelo probabilístico denominado Exponencial Geométrico (EG), que oferece uma grande exibilidade para a estimação estatística de seus parâmetros com base em amostras de dados de tempo de vida completos e censurados. Neste estudo são explorados os conceitos de estimadores e dados de tempo de vida sob censuras aleatórias em dois casos de extensões do modelo EG: o Exponencial Geom étrico Estendido (EEG) e o Exponencial Geométrico Extremo Generalizado (GE2). O trabalho ainda considera, exclusivamente para o modelo EEG, a abordagem de presença de covariáveis indexadas no parâmetro de taxa como uma segunda fonte de variação para acrescentar ainda mais exibilidade para o modelo, bem como, exclusivamente para o modelo GE2, uma análise de convergência até então ignorada, é proposta para seus momentos. A abordagem da inferência estatística é realizada para essas extensões no intuito de expor (no contexto clássico) seus estimadores de máxima verossimilhança e intervalos de con ança assintóticos, e (no contexto bayesiano) suas distribuições à priori e posteriori, ambos os casos para estimar seus parâmetros sob as censuras aleatórias, e covariáveis no caso do EEG. Neste trabalho os estimadores bayesianos são desenvolvidos com os pressupostos de que as prioris são vagas, seguem uma distribuição Gama e são independentes entre os parâmetros desconhecidos. Os resultados deste trabalho são resguardados de um estudo detalhado de simulação estatística aplicado para comparar os procedimentos de estimação abordados sob o pretexto de avaliar estes estimadores com base na probabilidade de 95% de cobertura, erro quadrático médio, vício médio e a amplitude intervalar média. Ao nal da abordagem de cada extensão é apresentada ainda uma aplicação com dados reais para destacar o alcance e as particularidades do modelo estendido abordado.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)CAPES: 88882.441640/2019-01Universidade Estadual Paulista (Unesp)Moala, Fernando Antonio [UNESP]Universidade Estadual Paulista (Unesp)Gianfelice, Paulo Roberto de Lima [UNESP]2020-07-08T13:24:05Z2020-07-08T13:24:05Z2020-02-26info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfapplication/pdfhttp://hdl.handle.net/11449/19292400093189533004129046P916212695523666970000-0002-2445-0407enginfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESP2023-10-27T06:09:38Zoai:repositorio.unesp.br:11449/192924Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-27T06:09:38Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored Inferência bayesiana e clássica para extensões da distribuição Exponencial Geométrica com aplicações em análise de sobrevivência sob dados covariados e aleatoriamente censurados |
title |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
spellingShingle |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored Gianfelice, Paulo Roberto de Lima [UNESP] Censored and covariate data Maximum likelihood and bayesian estimation Extensions for Exponential Geometric distribution Statistical simulation Dados censurados e covariados Estimação de máxima verossimilhança e bayesiano Extensões para a distribuição Exponencial Geométrica Simulação estatística |
title_short |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
title_full |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
title_fullStr |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
title_full_unstemmed |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
title_sort |
Bayesian and classical inference for extensions of Geometric Exponential distribution with applications in survival analysis under the presence of the data covariated and randomly censored |
author |
Gianfelice, Paulo Roberto de Lima [UNESP] |
author_facet |
Gianfelice, Paulo Roberto de Lima [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Moala, Fernando Antonio [UNESP] Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Gianfelice, Paulo Roberto de Lima [UNESP] |
dc.subject.por.fl_str_mv |
Censored and covariate data Maximum likelihood and bayesian estimation Extensions for Exponential Geometric distribution Statistical simulation Dados censurados e covariados Estimação de máxima verossimilhança e bayesiano Extensões para a distribuição Exponencial Geométrica Simulação estatística |
topic |
Censored and covariate data Maximum likelihood and bayesian estimation Extensions for Exponential Geometric distribution Statistical simulation Dados censurados e covariados Estimação de máxima verossimilhança e bayesiano Extensões para a distribuição Exponencial Geométrica Simulação estatística |
description |
This work presents a study of probabilistic modeling, with applications to survival analysis, based on a probabilistic model called Exponential Geometric (EG), which o ers great exibility for the statistical estimation of its parameters based on samples of life time data complete and censored. In this study, the concepts of estimators and lifetime data are explored under random censorship in two cases of extensions of the EG model: the Extended Geometric Exponential (EEG) and the Generalized Extreme Geometric Exponential (GE2). The work still considers, exclusively for the EEG model, the approach of the presence of covariates indexed in the rate parameter as a second source of variation to add even more exibility to the model, as well as, exclusively for the GE2 model, a analysis of the convergence, hitherto ignored, it is proposed for its moments. The statistical inference approach is performed for these extensions in order to expose (in the classical context) their maximum likelihood estimators and asymptotic con dence intervals, and (in the bayesian context) their a priori and a posteriori distributions, both cases to estimate their parameters under random censorship, and covariates in the case of EEG. In this work, bayesian estimators are developed with the assumptions that the prioris are vague, follow a Gamma distribution and are independent between the unknown parameters. The results of this work are regarded from a detailed study of statistical simulation applied to compare the estimation procedures approached under the pretext of evaluating these estimators based on the 95% coverage probability, mean square error, mean bias and the mean interval amplitude. At the end of each extension's approach, an application with real data is also presented to highlight the reach and particularities of the extended model addressed. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-07-08T13:24:05Z 2020-07-08T13:24:05Z 2020-02-26 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11449/192924 000931895 33004129046P9 1621269552366697 0000-0002-2445-0407 |
url |
http://hdl.handle.net/11449/192924 |
identifier_str_mv |
000931895 33004129046P9 1621269552366697 0000-0002-2445-0407 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
publisher.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964721538924544 |