Form-Invariance of the Non-Regular Exponential Family of Distributions

The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant w...

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Autores:
Ghorbanpour, Samereh
Chinipardaz, Rahim
Alavi, Seyed Mohammad Reza
Tipo de recurso:
Article of journal
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66484
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66484
http://bdigital.unal.edu.co/67512/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Fisher information matrix
Form-invariance
Non-regular exponential family
Maximum likelihood estimation
Weighted distribution
Distribución ponderada
estimación de m\'axima verosimilitud
familia exponencial no regular
invarianza de forma
matriz de información de Fisher
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Ghorbanpour, Samerehfcbaac1b-a670-4a65-993d-3f64a504d245300Chinipardaz, Rahim70ce8b27-a01c-42ee-8d55-437e80d9cf6d300Alavi, Seyed Mohammad Reza8a0be199-7bac-4916-81be-a7ca7e0d252f3002019-07-03T02:13:02Z2019-07-03T02:13:02Z2018-07-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66484http://bdigital.unal.edu.co/67512/The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.Las distribuciones ponderadas son usadas cuando el mecanismo de muestreo registra observaciones de acuerdo a una función no negativa. En ocasiones la forma de la función ponderada es igual a la original, excepto, posiblemente, en un cambio de parámetros y se denominan distribuciones ponderadas de forma invariante. En este artículo identificamos una clase general de funciones ponderadas e introducimos una forma extendida de distribuciones ponderadas de forma invariante, la cual incluye dos familias comunes: la familia exponencial y la familia no regular como caso particular. Algunas propiedades de estas distribuciones como las estadísticas suficientes y máximas suficientes, la estimación de máxima verosimilitud y la matriz de información de Fisher son estudiadas.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/62233Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaGhorbanpour, Samereh and Chinipardaz, Rahim and Alavi, Seyed Mohammad Reza (2018) Form-Invariance of the Non-Regular Exponential Family of Distributions. Revista Colombiana de Estadística, 41 (2). pp. 157-172. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsFisher information matrixForm-invarianceNon-regular exponential familyMaximum likelihood estimationWeighted distributionDistribución ponderadaestimación de m\'axima verosimilitudfamilia exponencial no regularinvarianza de formamatriz de información de FisherForm-Invariance of the Non-Regular Exponential Family of DistributionsArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL62233-390956-1-PB.pdfapplication/pdf633023https://repositorio.unal.edu.co/bitstream/unal/66484/1/62233-390956-1-PB.pdf4dc08a9ddf1c3987d1f90807a4f21d0aMD51THUMBNAIL62233-390956-1-PB.pdf.jpg62233-390956-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg6750https://repositorio.unal.edu.co/bitstream/unal/66484/2/62233-390956-1-PB.pdf.jpg6df8ccbb68a9a236147a2955a50296dfMD52unal/66484oai:repositorio.unal.edu.co:unal/664842023-05-25 23:02:53.46Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv Form-Invariance of the Non-Regular Exponential Family of Distributions
title Form-Invariance of the Non-Regular Exponential Family of Distributions
spellingShingle Form-Invariance of the Non-Regular Exponential Family of Distributions
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Fisher information matrix
Form-invariance
Non-regular exponential family
Maximum likelihood estimation
Weighted distribution
Distribución ponderada
estimación de m\'axima verosimilitud
familia exponencial no regular
invarianza de forma
matriz de información de Fisher
title_short Form-Invariance of the Non-Regular Exponential Family of Distributions
title_full Form-Invariance of the Non-Regular Exponential Family of Distributions
title_fullStr Form-Invariance of the Non-Regular Exponential Family of Distributions
title_full_unstemmed Form-Invariance of the Non-Regular Exponential Family of Distributions
title_sort Form-Invariance of the Non-Regular Exponential Family of Distributions
dc.creator.fl_str_mv Ghorbanpour, Samereh
Chinipardaz, Rahim
Alavi, Seyed Mohammad Reza
dc.contributor.author.spa.fl_str_mv Ghorbanpour, Samereh
Chinipardaz, Rahim
Alavi, Seyed Mohammad Reza
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
topic 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Fisher information matrix
Form-invariance
Non-regular exponential family
Maximum likelihood estimation
Weighted distribution
Distribución ponderada
estimación de m\'axima verosimilitud
familia exponencial no regular
invarianza de forma
matriz de información de Fisher
dc.subject.proposal.spa.fl_str_mv Fisher information matrix
Form-invariance
Non-regular exponential family
Maximum likelihood estimation
Weighted distribution
Distribución ponderada
estimación de m\'axima verosimilitud
familia exponencial no regular
invarianza de forma
matriz de información de Fisher
description The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018-07-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:13:02Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:13:02Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.type.content.spa.fl_str_mv Text
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status_str publishedVersion
dc.identifier.issn.spa.fl_str_mv ISSN: 2389-8976
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66484
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/67512/
identifier_str_mv ISSN: 2389-8976
url https://repositorio.unal.edu.co/handle/unal/66484
http://bdigital.unal.edu.co/67512/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/estad/article/view/62233
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística
Revista Colombiana de Estadística
dc.relation.references.spa.fl_str_mv Ghorbanpour, Samereh and Chinipardaz, Rahim and Alavi, Seyed Mohammad Reza (2018) Form-Invariance of the Non-Regular Exponential Family of Distributions. Revista Colombiana de Estadística, 41 (2). pp. 157-172. ISSN 2389-8976
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
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dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística
institution Universidad Nacional de Colombia
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