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

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dc.contributor.authorDey, Sanku
dc.contributor.authorMoala, Fernando A. [UNESP]
dc.contributor.authorKumar, Devendra
dc.contributor.institutionSt Anthonys Coll
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionCent Univ Haryana
dc.date.accessioned2018-11-26T16:04:40Z
dc.date.available2018-11-26T16:04:40Z
dc.date.issued2018-01-01
dc.description.abstractThis 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.en
dc.description.affiliationSt Anthonys Coll, Dept Stat, Shillong 793001, Meghalaya, India
dc.description.affiliationState Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil
dc.description.affiliationCent Univ Haryana, Dept Stat, Mahendergarh 123031, Haryana, India
dc.description.affiliationUnespState Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil
dc.format.extent839-876
dc.identifierhttp://dx.doi.org/10.1080/09720510.2018.1450197
dc.identifier.citationJournal Of Statistics & Management Systems. New Delhi: Taru Publications, v. 21, n. 5, p. 839-876, 2018.
dc.identifier.doi10.1080/09720510.2018.1450197
dc.identifier.fileWOS000440968500008.pdf
dc.identifier.issn0972-0510
dc.identifier.lattes1621269552366697
dc.identifier.orcid0000-0002-2445-0407
dc.identifier.urihttp://hdl.handle.net/11449/160483
dc.identifier.wosWOS:000440968500008
dc.language.isoeng
dc.publisherTaru Publications
dc.relation.ispartofJournal Of Statistics & Management Systems
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.subjectBayes estimator
dc.subjectMaximum likelihood estimators
dc.subjectMoment estimators
dc.subjectMinimum distances estimators
dc.subjectFailure rate function
dc.subjectMean residual life function
dc.titleStatistical properties and different methods of estimation of Gompertz distribution with applicationen
dc.typeArtigo
dcterms.rightsHolderTaru Publications
unesp.author.lattes1621269552366697[2]
unesp.author.orcid0000-0002-2445-0407[2]

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