Distribution of the product of independent extended beta variables

ABSTRACT: The extended beta type 1 distribution has the probability density function proportional to x α−1 (1−x) β−1 exp[−σ/x(1−x)], 0 < x < 1. In this article, we derive the probability density function of the product of two independent random variables each having an extended beta type 1 dis...

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Autores:
Nagar, Daya Krishna
Zarrazola Rivera, Edwin de Jesús
Sánchez Herrera, Luz Estela
Tipo de recurso:
Article of investigation
Fecha de publicación:
2014
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/26792
Acceso en línea:
http://hdl.handle.net/10495/26792
Palabra clave:
Funciones hipergeométricas
Hypergeometric functions
Beta distribution
Extended beta function
Gamma distribution
Gauss hypergeometric function
Inverted gamma distribution
Rights
openAccess
License
http://creativecommons.org/licenses/by/2.5/co/
id UDEA2_99157abb3ac10313912b45ba0f3346ff
oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/26792
network_acronym_str UDEA2
network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv Distribution of the product of independent extended beta variables
title Distribution of the product of independent extended beta variables
spellingShingle Distribution of the product of independent extended beta variables
Funciones hipergeométricas
Hypergeometric functions
Beta distribution
Extended beta function
Gamma distribution
Gauss hypergeometric function
Inverted gamma distribution
title_short Distribution of the product of independent extended beta variables
title_full Distribution of the product of independent extended beta variables
title_fullStr Distribution of the product of independent extended beta variables
title_full_unstemmed Distribution of the product of independent extended beta variables
title_sort Distribution of the product of independent extended beta variables
dc.creator.fl_str_mv Nagar, Daya Krishna
Zarrazola Rivera, Edwin de Jesús
Sánchez Herrera, Luz Estela
dc.contributor.author.none.fl_str_mv Nagar, Daya Krishna
Zarrazola Rivera, Edwin de Jesús
Sánchez Herrera, Luz Estela
dc.subject.lemb.none.fl_str_mv Funciones hipergeométricas
Hypergeometric functions
topic Funciones hipergeométricas
Hypergeometric functions
Beta distribution
Extended beta function
Gamma distribution
Gauss hypergeometric function
Inverted gamma distribution
dc.subject.proposal.spa.fl_str_mv Beta distribution
Extended beta function
Gamma distribution
Gauss hypergeometric function
Inverted gamma distribution
description ABSTRACT: The extended beta type 1 distribution has the probability density function proportional to x α−1 (1−x) β−1 exp[−σ/x(1−x)], 0 < x < 1. In this article, we derive the probability density function of the product of two independent random variables each having an extended beta type 1 distribution. We also consider several other products involving extended beta type 1, beta type 1, beta type 2, beta type 3, Kummer-beta and inverted gamma variables.
publishDate 2014
dc.date.issued.none.fl_str_mv 2014
dc.date.accessioned.none.fl_str_mv 2022-03-22T21:38:46Z
dc.date.available.none.fl_str_mv 2022-03-22T21:38:46Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
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dc.type.redcol.spa.fl_str_mv https://purl.org/redcol/resource_type/ART
dc.type.local.spa.fl_str_mv Artículo de investigación
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dc.identifier.citation.spa.fl_str_mv Nagar, D., Zarrazola, E., & Sánchez, L. (2014). Distribution of the product of independent extended beta variables. Applied Mathematical Sciences, 8(161), 8007-8019. http://dx.doi.org/10.12988/ams.2014.410814
dc.identifier.issn.none.fl_str_mv 1312-885X
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10495/26792
dc.identifier.doi.none.fl_str_mv 10.12988/ams.2014.410814
dc.identifier.eissn.none.fl_str_mv 1314-7552
identifier_str_mv Nagar, D., Zarrazola, E., & Sánchez, L. (2014). Distribution of the product of independent extended beta variables. Applied Mathematical Sciences, 8(161), 8007-8019. http://dx.doi.org/10.12988/ams.2014.410814
1312-885X
10.12988/ams.2014.410814
1314-7552
url http://hdl.handle.net/10495/26792
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournalabbrev.spa.fl_str_mv Appl. Math. Sci.
dc.rights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by/2.5/co/
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dc.rights.creativecommons.spa.fl_str_mv https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
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dc.publisher.spa.fl_str_mv Hikari
dc.publisher.group.spa.fl_str_mv Análisis Multivariado
dc.publisher.place.spa.fl_str_mv Bulgaria
institution Universidad de Antioquia
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spelling Nagar, Daya KrishnaZarrazola Rivera, Edwin de JesúsSánchez Herrera, Luz Estela2022-03-22T21:38:46Z2022-03-22T21:38:46Z2014Nagar, D., Zarrazola, E., & Sánchez, L. (2014). Distribution of the product of independent extended beta variables. Applied Mathematical Sciences, 8(161), 8007-8019. http://dx.doi.org/10.12988/ams.2014.4108141312-885Xhttp://hdl.handle.net/10495/2679210.12988/ams.2014.4108141314-7552ABSTRACT: The extended beta type 1 distribution has the probability density function proportional to x α−1 (1−x) β−1 exp[−σ/x(1−x)], 0 < x < 1. In this article, we derive the probability density function of the product of two independent random variables each having an extended beta type 1 distribution. We also consider several other products involving extended beta type 1, beta type 1, beta type 2, beta type 3, Kummer-beta and inverted gamma variables.COL000053213application/pdfengHikariAnálisis MultivariadoBulgariainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Distribution of the product of independent extended beta variablesFunciones hipergeométricasHypergeometric functionsBeta distributionExtended beta functionGamma distributionGauss hypergeometric functionInverted gamma distributionAppl. Math. Sci.Applied Mathematical Sciences800780198161ORIGINALNagarDaya_2014_ProductIndependentBeta.pdfNagarDaya_2014_ProductIndependentBeta.pdfArtículo de investigaciónapplication/pdf216148https://bibliotecadigital.udea.edu.co/bitstream/10495/26792/1/NagarDaya_2014_ProductIndependentBeta.pdf760b0fffbc0c8179246fa4d363515e04MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstream/10495/26792/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/26792/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/26792oai:bibliotecadigital.udea.edu.co:10495/267922023-04-11 16:13:30.639Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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