Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/59401 |
Resumo: | The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas. |
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Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustnessLikelihood-based methodsBootstrappingStudent-t distributionR computer languageLogistic distributionMonte Carlo simulationlogisticnormal and Student-t distributionsCiências Naturais::MatemáticasScience & TechnologyThe Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas.Emilia Athayde and Assis Azevedo were partially supported by the Research Centre of Mathematics of the University ofMinho with the Portuguese Funds from the “Fundaçao para a Ciência e a Tecnologia”, through the Project UID/MAT/00013/2013. Michelli Barros was partially supported by the Brazilian Council for Scientific and Technological Development (CNPq in Portuguese). Victor Leiva was partially supported by the Chilean Council for Scientific and Technology Research (Conicyt in Spanish), grant FONDECYT1160868.info:eu-repo/semantics/publishedVersionBrazilian Statistical AssociationUniversidade do MinhoAthayde, EmiliaAzevedo, AssisBarros, MichelliLeiva, Víctor2019-032019-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/59401eng0103-07520103-075210.1214/17-BJPS389https://doi.org/10.1214/17-BJPS389info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:29:43Zoai:repositorium.sdum.uminho.pt:1822/59401Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:24:44.888694Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
title |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
spellingShingle |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness Athayde, Emilia Likelihood-based methods Bootstrapping Student-t distribution R computer language Logistic distribution Monte Carlo simulation logistic normal and Student-t distributions Ciências Naturais::Matemáticas Science & Technology |
title_short |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
title_full |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
title_fullStr |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
title_full_unstemmed |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
title_sort |
Failure rate of Birnbaum–Saunders distributions: shape, change-point, estimation and robustness |
author |
Athayde, Emilia |
author_facet |
Athayde, Emilia Azevedo, Assis Barros, Michelli Leiva, Víctor |
author_role |
author |
author2 |
Azevedo, Assis Barros, Michelli Leiva, Víctor |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Athayde, Emilia Azevedo, Assis Barros, Michelli Leiva, Víctor |
dc.subject.por.fl_str_mv |
Likelihood-based methods Bootstrapping Student-t distribution R computer language Logistic distribution Monte Carlo simulation logistic normal and Student-t distributions Ciências Naturais::Matemáticas Science & Technology |
topic |
Likelihood-based methods Bootstrapping Student-t distribution R computer language Logistic distribution Monte Carlo simulation logistic normal and Student-t distributions Ciências Naturais::Matemáticas Science & Technology |
description |
The Birnbaum–Saunders (BS) distribution has been largely studied and applied. A random variable with BS distribution is a transformation of another random variable with standard normal distribution. Generalized BS distributions are obtained when the normally distributed random variable is replaced by another symmetrically distributed random variable. This allows us to obtain a wide class of positively skewed models with lighter and heavier tails than the BS model. Its failure rate admits several shapes, including the unimodal case, with its change-point being able to be used for different purposes. For example, to establish the reduction in a dose, and then in the cost of the medical treatment. We analyze the failure rates of generalized BS distributions obtained by the logistic, normal and Student-t distributions, considering their shape and change-point, estimating them, evaluating their robustness, assessing their performance by simulations, and applying the results to real data from different areas. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-03 2019-03-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/59401 |
url |
http://hdl.handle.net/1822/59401 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0103-0752 0103-0752 10.1214/17-BJPS389 https://doi.org/10.1214/17-BJPS389 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Brazilian Statistical Association |
publisher.none.fl_str_mv |
Brazilian Statistical Association |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799132729071108096 |