Objective and subjective prior distributions for the gompertz distribution
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1590/0001-3765201820171040 http://hdl.handle.net/11449/188175 |
Resumo: | This paper takes into account the estimation for the unknown parameters of the Gompertz distribution from the frequentist and Bayesian view points by using both objective and subjective prior distributions. We first derive non-informative priors using formal rules, such as Jefreys prior and maximal data information prior (MDIP), based on Fisher information and entropy, respectively. We also propose a prior distribution that incorporate the expert’s knowledge about the issue under study. In this regard, we assume two independent gamma distributions for the parameters of the Gompertz distribution and it is employed for an elicitation process based on the predictive prior distribution by using Laplace approximation for integrals. We suppose that an expert can summarize his/her knowledge about the reliability of an item through statements of percentiles. We also present a set of priors proposed by Singpurwala assuming a truncated normal prior distribution for the median of distribution and a gamma prior for the scale parameter. Next, we investigate the effects of these priors in the posterior estimates of the parameters of the Gompertz distribution. The Bayes estimates are computed using Markov Chain Monte Carlo (MCMC) algorithm. An extensive numerical simulation is carried out to evaluate the performance of the maximum likelihood estimates and Bayes estimates based on bias, mean-squared error and coverage probabilities. Finally, a real data set have been analyzed for illustrative purposes. |
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Objective and subjective prior distributions for the gompertz distributionElicitationGompertz distributionJeffreys priorMaximal data information priorObjective priorSubjective priorThis paper takes into account the estimation for the unknown parameters of the Gompertz distribution from the frequentist and Bayesian view points by using both objective and subjective prior distributions. We first derive non-informative priors using formal rules, such as Jefreys prior and maximal data information prior (MDIP), based on Fisher information and entropy, respectively. We also propose a prior distribution that incorporate the expert’s knowledge about the issue under study. In this regard, we assume two independent gamma distributions for the parameters of the Gompertz distribution and it is employed for an elicitation process based on the predictive prior distribution by using Laplace approximation for integrals. We suppose that an expert can summarize his/her knowledge about the reliability of an item through statements of percentiles. We also present a set of priors proposed by Singpurwala assuming a truncated normal prior distribution for the median of distribution and a gamma prior for the scale parameter. Next, we investigate the effects of these priors in the posterior estimates of the parameters of the Gompertz distribution. The Bayes estimates are computed using Markov Chain Monte Carlo (MCMC) algorithm. An extensive numerical simulation is carried out to evaluate the performance of the maximum likelihood estimates and Bayes estimates based on bias, mean-squared error and coverage probabilities. Finally, a real data set have been analyzed for illustrative purposes.Departamento de Estatística Faculdade de Ciências e Tecnologia Universidade Estadual Paulista/UNESP Rua Roberto Simonsen, 305, Centro EducacionalDepartment of Statistics St. Anthony’s College, Bomfyle road, East Khasi HillsDepartamento de Estatística Faculdade de Ciências e Tecnologia Universidade Estadual Paulista/UNESP Rua Roberto Simonsen, 305, Centro EducacionalUniversidade Estadual Paulista (Unesp)St. Anthony’s CollegeMoala, Fernando A. [UNESP]Dey, Sanku2019-10-06T15:59:41Z2019-10-06T15:59:41Z2018-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2643-2661application/pdfhttp://dx.doi.org/10.1590/0001-3765201820171040Anais da Academia Brasileira de Ciencias, v. 90, n. 3, p. 2643-2661, 2018.1678-26900001-3765http://hdl.handle.net/11449/18817510.1590/0001-3765201820171040S0001-376520180006026432-s2.0-85054562013S0001-37652018000602643.pdf16212695523666970000-0002-2445-0407Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAnais da Academia Brasileira de Cienciasinfo:eu-repo/semantics/openAccess2023-10-14T06:03:25Zoai:repositorio.unesp.br:11449/188175Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-14T06:03:25Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Objective and subjective prior distributions for the gompertz distribution |
title |
Objective and subjective prior distributions for the gompertz distribution |
spellingShingle |
Objective and subjective prior distributions for the gompertz distribution Moala, Fernando A. [UNESP] Elicitation Gompertz distribution Jeffreys prior Maximal data information prior Objective prior Subjective prior |
title_short |
Objective and subjective prior distributions for the gompertz distribution |
title_full |
Objective and subjective prior distributions for the gompertz distribution |
title_fullStr |
Objective and subjective prior distributions for the gompertz distribution |
title_full_unstemmed |
Objective and subjective prior distributions for the gompertz distribution |
title_sort |
Objective and subjective prior distributions for the gompertz distribution |
author |
Moala, Fernando A. [UNESP] |
author_facet |
Moala, Fernando A. [UNESP] Dey, Sanku |
author_role |
author |
author2 |
Dey, Sanku |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) St. Anthony’s College |
dc.contributor.author.fl_str_mv |
Moala, Fernando A. [UNESP] Dey, Sanku |
dc.subject.por.fl_str_mv |
Elicitation Gompertz distribution Jeffreys prior Maximal data information prior Objective prior Subjective prior |
topic |
Elicitation Gompertz distribution Jeffreys prior Maximal data information prior Objective prior Subjective prior |
description |
This paper takes into account the estimation for the unknown parameters of the Gompertz distribution from the frequentist and Bayesian view points by using both objective and subjective prior distributions. We first derive non-informative priors using formal rules, such as Jefreys prior and maximal data information prior (MDIP), based on Fisher information and entropy, respectively. We also propose a prior distribution that incorporate the expert’s knowledge about the issue under study. In this regard, we assume two independent gamma distributions for the parameters of the Gompertz distribution and it is employed for an elicitation process based on the predictive prior distribution by using Laplace approximation for integrals. We suppose that an expert can summarize his/her knowledge about the reliability of an item through statements of percentiles. We also present a set of priors proposed by Singpurwala assuming a truncated normal prior distribution for the median of distribution and a gamma prior for the scale parameter. Next, we investigate the effects of these priors in the posterior estimates of the parameters of the Gompertz distribution. The Bayes estimates are computed using Markov Chain Monte Carlo (MCMC) algorithm. An extensive numerical simulation is carried out to evaluate the performance of the maximum likelihood estimates and Bayes estimates based on bias, mean-squared error and coverage probabilities. Finally, a real data set have been analyzed for illustrative purposes. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-07-01 2019-10-06T15:59:41Z 2019-10-06T15:59:41Z |
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://dx.doi.org/10.1590/0001-3765201820171040 Anais da Academia Brasileira de Ciencias, v. 90, n. 3, p. 2643-2661, 2018. 1678-2690 0001-3765 http://hdl.handle.net/11449/188175 10.1590/0001-3765201820171040 S0001-37652018000602643 2-s2.0-85054562013 S0001-37652018000602643.pdf 1621269552366697 0000-0002-2445-0407 |
url |
http://dx.doi.org/10.1590/0001-3765201820171040 http://hdl.handle.net/11449/188175 |
identifier_str_mv |
Anais da Academia Brasileira de Ciencias, v. 90, n. 3, p. 2643-2661, 2018. 1678-2690 0001-3765 10.1590/0001-3765201820171040 S0001-37652018000602643 2-s2.0-85054562013 S0001-37652018000602643.pdf 1621269552366697 0000-0002-2445-0407 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Anais da Academia Brasileira de Ciencias |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2643-2661 application/pdf |
dc.source.none.fl_str_mv |
Scopus 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_ |
1799964553616818176 |