Statistical properties and different methods of estimation of Gompertz distribution with application

Detalhes bibliográficos
Autor(a) principal: Dey, Sanku
Data de Publicação: 2018
Outros Autores: Moala, Fernando A. [UNESP], Kumar, Devendra
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1080/09720510.2018.1450197
http://hdl.handle.net/11449/160483
Resumo: This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stress-strength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimator, Cramer-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Coverage probabilities for the frequentist methods are also obtained. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using gamma priors for both shape and scale parameters. Furthermore, the Bayes estimators and their respective posterior risks are computed and compared using MCMC algorithm. Finally, a real data set have been analyzed for illustrative purposes.
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spelling Statistical properties and different methods of estimation of Gompertz distribution with applicationBayes estimatorMaximum likelihood estimatorsMoment estimatorsMinimum distances estimatorsFailure rate functionMean residual life functionThis article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stress-strength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimator, Cramer-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Coverage probabilities for the frequentist methods are also obtained. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using gamma priors for both shape and scale parameters. Furthermore, the Bayes estimators and their respective posterior risks are computed and compared using MCMC algorithm. Finally, a real data set have been analyzed for illustrative purposes.St Anthonys Coll, Dept Stat, Shillong 793001, Meghalaya, IndiaState Univ Sao Paulo, Dept Stat, Sao Paulo, BrazilCent Univ Haryana, Dept Stat, Mahendergarh 123031, Haryana, IndiaState Univ Sao Paulo, Dept Stat, Sao Paulo, BrazilTaru PublicationsSt Anthonys CollUniversidade Estadual Paulista (Unesp)Cent Univ HaryanaDey, SankuMoala, Fernando A. [UNESP]Kumar, Devendra2018-11-26T16:04:40Z2018-11-26T16:04:40Z2018-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article839-876application/pdfhttp://dx.doi.org/10.1080/09720510.2018.1450197Journal Of Statistics & Management Systems. New Delhi: Taru Publications, v. 21, n. 5, p. 839-876, 2018.0972-0510http://hdl.handle.net/11449/16048310.1080/09720510.2018.1450197WOS:000440968500008WOS000440968500008.pdf16212695523666970000-0002-2445-0407Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Statistics & Management Systemsinfo:eu-repo/semantics/openAccess2023-10-09T06:07:31Zoai:repositorio.unesp.br:11449/160483Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:28:45.980320Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Statistical properties and different methods of estimation of Gompertz distribution with application
title Statistical properties and different methods of estimation of Gompertz distribution with application
spellingShingle Statistical properties and different methods of estimation of Gompertz distribution with application
Dey, Sanku
Bayes estimator
Maximum likelihood estimators
Moment estimators
Minimum distances estimators
Failure rate function
Mean residual life function
title_short Statistical properties and different methods of estimation of Gompertz distribution with application
title_full Statistical properties and different methods of estimation of Gompertz distribution with application
title_fullStr Statistical properties and different methods of estimation of Gompertz distribution with application
title_full_unstemmed Statistical properties and different methods of estimation of Gompertz distribution with application
title_sort Statistical properties and different methods of estimation of Gompertz distribution with application
author Dey, Sanku
author_facet Dey, Sanku
Moala, Fernando A. [UNESP]
Kumar, Devendra
author_role author
author2 Moala, Fernando A. [UNESP]
Kumar, Devendra
author2_role author
author
dc.contributor.none.fl_str_mv St Anthonys Coll
Universidade Estadual Paulista (Unesp)
Cent Univ Haryana
dc.contributor.author.fl_str_mv Dey, Sanku
Moala, Fernando A. [UNESP]
Kumar, Devendra
dc.subject.por.fl_str_mv Bayes estimator
Maximum likelihood estimators
Moment estimators
Minimum distances estimators
Failure rate function
Mean residual life function
topic Bayes estimator
Maximum likelihood estimators
Moment estimators
Minimum distances estimators
Failure rate function
Mean residual life function
description This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stress-strength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimator, Cramer-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Coverage probabilities for the frequentist methods are also obtained. Next we consider Bayes estimation under different types of loss function (symmetric and asymmetric loss functions) using gamma priors for both shape and scale parameters. Furthermore, the Bayes estimators and their respective posterior risks are computed and compared using MCMC algorithm. Finally, a real data set have been analyzed for illustrative purposes.
publishDate 2018
dc.date.none.fl_str_mv 2018-11-26T16:04:40Z
2018-11-26T16:04:40Z
2018-01-01
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/10.1080/09720510.2018.1450197
Journal Of Statistics & Management Systems. New Delhi: Taru Publications, v. 21, n. 5, p. 839-876, 2018.
0972-0510
http://hdl.handle.net/11449/160483
10.1080/09720510.2018.1450197
WOS:000440968500008
WOS000440968500008.pdf
1621269552366697
0000-0002-2445-0407
url http://dx.doi.org/10.1080/09720510.2018.1450197
http://hdl.handle.net/11449/160483
identifier_str_mv Journal Of Statistics & Management Systems. New Delhi: Taru Publications, v. 21, n. 5, p. 839-876, 2018.
0972-0510
10.1080/09720510.2018.1450197
WOS:000440968500008
WOS000440968500008.pdf
1621269552366697
0000-0002-2445-0407
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal Of Statistics & Management Systems
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 839-876
application/pdf
dc.publisher.none.fl_str_mv Taru Publications
publisher.none.fl_str_mv Taru Publications
dc.source.none.fl_str_mv Web of Science
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_ 1808128364706267136