Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/33110 |
Resumo: | The Cauchy-Rayleigh (CR) distribution has been successfully used to describe asymmetrical and heavy-tail events from radar imagery. Employing such model to describe lifetime data may then seem attractive, but drawbacks arise: its probability density function does not cover non-modal behavior as well as its hazard rate function (hrf) assumes only one form. To outperform this difficulty, it is investigated the exponentiated Cauchy-Rayleigh (ECR) distribution. This byparameteric model is flexible enough to accommodate hrf with decreasing, decreasing-increasing-decreasing and upside-down bathtub forms. Several closed-form mathematical expressions for the ECR model are obtained: median, mode, some moments, (h;Φ)-entropies and Fisher information matrix. Their non-existence respective cases are also determined. It is proposed two estimators for the ECR parameters: maximum likelihood (ML) and percentile-based methods. Both of this methods may be biased for small and moderate sample sizes. To overcome it we furnish a expression for its second-order bias according to Cox and Snell (1968) and propose a third bias-corrected ML estimator. Further discussions about hypotheses-based inference and estimation formulas on censored-data are furnished as well. A simulation study is done to assess the estimators performance. The estimates existence and uniqueness are not guaranteed, thus procedures to constrained estimation are developed to overcome this trouble. Notes about hypothesis tests are given under censored and uncensored schemes. An application in a survival dataset illustrates the proposed model usefulness. Results point out that the ECR distribution may outperform classical lifetime biparametric models, such as the gamma, Birnbaum-Saunders, Weibull and log-normal laws, before heavy-tail data. The likelihood ratio test are compared against entropy-based tests as urban texture detector using a San Francisco synthetic aperture radar imagery. This same image is also the final application target which consist of compare segmentation algorithms based on CR and ECR entropies densities finite mixture. It is recurred to a result due Pardo et al. (1997) which provides the (h;Φ)-entropies asymptotic distribution. The finite mixture log-likelihood function is maximized using the Expectation-Maximization algorithm. |
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VEDOVATTO, Thiagohttp://lattes.cnpq.br/1555798555635250http://lattes.cnpq.br/9853084384672692NASCIMENTO, Abraão David Costa do2019-09-17T21:33:49Z2019-09-17T21:33:49Z2019-02-25https://repositorio.ufpe.br/handle/123456789/33110The Cauchy-Rayleigh (CR) distribution has been successfully used to describe asymmetrical and heavy-tail events from radar imagery. Employing such model to describe lifetime data may then seem attractive, but drawbacks arise: its probability density function does not cover non-modal behavior as well as its hazard rate function (hrf) assumes only one form. To outperform this difficulty, it is investigated the exponentiated Cauchy-Rayleigh (ECR) distribution. This byparameteric model is flexible enough to accommodate hrf with decreasing, decreasing-increasing-decreasing and upside-down bathtub forms. Several closed-form mathematical expressions for the ECR model are obtained: median, mode, some moments, (h;Φ)-entropies and Fisher information matrix. Their non-existence respective cases are also determined. It is proposed two estimators for the ECR parameters: maximum likelihood (ML) and percentile-based methods. Both of this methods may be biased for small and moderate sample sizes. To overcome it we furnish a expression for its second-order bias according to Cox and Snell (1968) and propose a third bias-corrected ML estimator. Further discussions about hypotheses-based inference and estimation formulas on censored-data are furnished as well. A simulation study is done to assess the estimators performance. The estimates existence and uniqueness are not guaranteed, thus procedures to constrained estimation are developed to overcome this trouble. Notes about hypothesis tests are given under censored and uncensored schemes. An application in a survival dataset illustrates the proposed model usefulness. Results point out that the ECR distribution may outperform classical lifetime biparametric models, such as the gamma, Birnbaum-Saunders, Weibull and log-normal laws, before heavy-tail data. The likelihood ratio test are compared against entropy-based tests as urban texture detector using a San Francisco synthetic aperture radar imagery. This same image is also the final application target which consist of compare segmentation algorithms based on CR and ECR entropies densities finite mixture. It is recurred to a result due Pardo et al. (1997) which provides the (h;Φ)-entropies asymptotic distribution. The finite mixture log-likelihood function is maximized using the Expectation-Maximization algorithm.IFGA distribuição de Cauchy-Rayleigh (CR) tem sido usada com sucesso para descrever dados assimétricos e eventos com caudas pesadas de imagens de radar. Empregar tal modelo para descrever dados de sobrevivência poder ser atrativo, mas inconvenientes surgem: sua função de densidade de probabilidade não abriga comportamento amodal bem como sua função de taxa de falha (hrf) assume apenas uma forma. Para superar essa dificuldade, é investigada a distribuição Cauchy-Rayleigh exponencializada (ECR). Este modelo biparamétrico é flexivel o bastante para acomodar hrf com formas decrescente, decrescente-crescente-decrescente e banheira invertida. Várias expressões matemáticas em forma fechada para o modelo ECR são obtidas: mediana, moda, alguns momentos, (h;Φ)-entropias e matriz de informação de Fisher. Seus respectivos casos de não existência também são determinados. São propostos dois estimadores para os parâmetros da ECR: métodos de máxima verossimilhança (ML) e estimação quantílica. Ambos os métodos podem ser viesados para tamanhos de amostra pequenos e moderados. Para superar isto, fornecemos uma expressão para o viés de segunda ordem de acordo com Cox e Snell (1968) e propusemos um estimador de máxima verossimilhança com viés de terceira ordem corrigido. Discussões adicionais sobre inferência baseada em hipóteses e fórmulas de estimação em dados censurados são fornecidas. Um estudo de simulação é feito para aferir a performance dos estimadores. A existência e unicidade das estimativas não é garantida, assim procedimentos para estimação restrita são desenvolvidos para superar esse problema. Notas sobre teste de hipótese são dadas considerando esquemas censurados e não-censurados. Uma aplicação em dados de sobrevida ilustra a utilidade do modelo proposto. Os resultados apontam que a distribuição ECR pode superar modelos biparamétricos de sobrevivência clássicos como gama, Birnbaum-Saunders, Weibull e log-normal. O teste da razão de verossimilhança é comparado com testes baseados em entropias como detector de texturas urbanas em uma imagem synthetic aperture radar da cidade de São Francisco. Esta mesma imagem é também alvo da aplicação final que consiste em comparar algorítmos de segmentação baseados em misturas finitas das densidades das entropias dos modelos CR e ECR. Recorremos a um resultado de Pardo et al. (1997) o qual nos dá distribuição assintótica das (h;Φ)-entropias. A função de log-verossimilhança das misturas finitas é maximizada usando o algorítmo EM.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/openAccessEstatísticaInferênciaProbabilidadeInference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed dataInference, information theory, and segmentation based on the extended Cauchy-Rayleigh model: applications to heavy-tailed datainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Thiago VedoVatto.pdf.jpgTESE Thiago VedoVatto.pdf.jpgGenerated Thumbnailimage/jpeg1372https://repositorio.ufpe.br/bitstream/123456789/33110/5/TESE%20Thiago%20VedoVatto.pdf.jpg1a7056fb3c0fe4a5fc31dcec6ba41a08MD55ORIGINALTESE Thiago VedoVatto.pdfTESE Thiago VedoVatto.pdfapplication/pdf9122405https://repositorio.ufpe.br/bitstream/123456789/33110/1/TESE%20Thiago%20VedoVatto.pdf443713a6f9ffc10db020c09dfa3750d1MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
dc.title.alternative.pt_BR.fl_str_mv |
Inference, information theory, and segmentation based on the extended Cauchy-Rayleigh model: applications to heavy-tailed data |
title |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
spellingShingle |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data VEDOVATTO, Thiago Estatística Inferência Probabilidade |
title_short |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
title_full |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
title_fullStr |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
title_full_unstemmed |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
title_sort |
Inference, information theory and segmentation based on an extended Cauchy-Rayleigh distribution : applications to heavy tailed data |
author |
VEDOVATTO, Thiago |
author_facet |
VEDOVATTO, Thiago |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/1555798555635250 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/9853084384672692 |
dc.contributor.author.fl_str_mv |
VEDOVATTO, Thiago |
dc.contributor.advisor1.fl_str_mv |
NASCIMENTO, Abraão David Costa do |
contributor_str_mv |
NASCIMENTO, Abraão David Costa do |
dc.subject.por.fl_str_mv |
Estatística Inferência Probabilidade |
topic |
Estatística Inferência Probabilidade |
description |
The Cauchy-Rayleigh (CR) distribution has been successfully used to describe asymmetrical and heavy-tail events from radar imagery. Employing such model to describe lifetime data may then seem attractive, but drawbacks arise: its probability density function does not cover non-modal behavior as well as its hazard rate function (hrf) assumes only one form. To outperform this difficulty, it is investigated the exponentiated Cauchy-Rayleigh (ECR) distribution. This byparameteric model is flexible enough to accommodate hrf with decreasing, decreasing-increasing-decreasing and upside-down bathtub forms. Several closed-form mathematical expressions for the ECR model are obtained: median, mode, some moments, (h;Φ)-entropies and Fisher information matrix. Their non-existence respective cases are also determined. It is proposed two estimators for the ECR parameters: maximum likelihood (ML) and percentile-based methods. Both of this methods may be biased for small and moderate sample sizes. To overcome it we furnish a expression for its second-order bias according to Cox and Snell (1968) and propose a third bias-corrected ML estimator. Further discussions about hypotheses-based inference and estimation formulas on censored-data are furnished as well. A simulation study is done to assess the estimators performance. The estimates existence and uniqueness are not guaranteed, thus procedures to constrained estimation are developed to overcome this trouble. Notes about hypothesis tests are given under censored and uncensored schemes. An application in a survival dataset illustrates the proposed model usefulness. Results point out that the ECR distribution may outperform classical lifetime biparametric models, such as the gamma, Birnbaum-Saunders, Weibull and log-normal laws, before heavy-tail data. The likelihood ratio test are compared against entropy-based tests as urban texture detector using a San Francisco synthetic aperture radar imagery. This same image is also the final application target which consist of compare segmentation algorithms based on CR and ECR entropies densities finite mixture. It is recurred to a result due Pardo et al. (1997) which provides the (h;Φ)-entropies asymptotic distribution. The finite mixture log-likelihood function is maximized using the Expectation-Maximization algorithm. |
publishDate |
2019 |
dc.date.accessioned.fl_str_mv |
2019-09-17T21:33:49Z |
dc.date.available.fl_str_mv |
2019-09-17T21:33:49Z |
dc.date.issued.fl_str_mv |
2019-02-25 |
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/123456789/33110 |
url |
https://repositorio.ufpe.br/handle/123456789/33110 |
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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