Bivariate generalization of the Gauss hypergeometric distribution
ABSTRACT: The bivariate generalization of the Gauss hypergeometric distribution is defined by the probability density function proportional to x α1−1y α2−1 (1 − x − y) β−1 (1 + ξ1x + ξ2y) −γ , x > 0, y > 0, x + y < 1, where αi > 0, i = 1, 2, β > 0, −∞ < γ < ∞ and ξi > −1, i =...
- Autores:
-
Nagar, Daya Krishna
Bedoya Valencia, Danilo
Gupta, Arjun Kumar
- 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:10495/26790
- Acceso en línea:
- http://hdl.handle.net/10495/26790
- Palabra clave:
- Funciones
Functions
Funciones hipergeométricas
Hypergeometric functions
62H15
62E15
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
| id |
UDEA2_dc08be6f9e16c586f0e0f8d6a5b2d373 |
|---|---|
| oai_identifier_str |
oai:bibliotecadigital.udea.edu.co:10495/26790 |
| network_acronym_str |
UDEA2 |
| network_name_str |
Repositorio UdeA |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
Bivariate generalization of the Gauss hypergeometric distribution |
| title |
Bivariate generalization of the Gauss hypergeometric distribution |
| spellingShingle |
Bivariate generalization of the Gauss hypergeometric distribution Funciones Functions Funciones hipergeométricas Hypergeometric functions 62H15 62E15 |
| title_short |
Bivariate generalization of the Gauss hypergeometric distribution |
| title_full |
Bivariate generalization of the Gauss hypergeometric distribution |
| title_fullStr |
Bivariate generalization of the Gauss hypergeometric distribution |
| title_full_unstemmed |
Bivariate generalization of the Gauss hypergeometric distribution |
| title_sort |
Bivariate generalization of the Gauss hypergeometric distribution |
| dc.creator.fl_str_mv |
Nagar, Daya Krishna Bedoya Valencia, Danilo Gupta, Arjun Kumar |
| dc.contributor.author.none.fl_str_mv |
Nagar, Daya Krishna Bedoya Valencia, Danilo Gupta, Arjun Kumar |
| dc.subject.lemb.none.fl_str_mv |
Funciones Functions Funciones hipergeométricas Hypergeometric functions |
| topic |
Funciones Functions Funciones hipergeométricas Hypergeometric functions 62H15 62E15 |
| dc.subject.proposal.spa.fl_str_mv |
62H15 62E15 |
| description |
ABSTRACT: The bivariate generalization of the Gauss hypergeometric distribution is defined by the probability density function proportional to x α1−1y α2−1 (1 − x − y) β−1 (1 + ξ1x + ξ2y) −γ , x > 0, y > 0, x + y < 1, where αi > 0, i = 1, 2, β > 0, −∞ < γ < ∞ and ξi > −1, i = 1, 2 are constants. In this article, we study several of its properties such as marginal and conditional distributions, joint moments and the coefficient of correlation. We compute the exact forms of R´enyi and Shannon entropies for this distribution. We also derive the distributions of X+Y , X/(X +Y ), V = X/Y and XY where X and Y follow a bivariate Gauss hypergeometric distribution. |
| publishDate |
2014 |
| dc.date.issued.none.fl_str_mv |
2014 |
| dc.date.accessioned.none.fl_str_mv |
2022-03-22T21:24:23Z |
| dc.date.available.none.fl_str_mv |
2022-03-22T21:24:23Z |
| dc.type.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.redcol.spa.fl_str_mv |
https://purl.org/redcol/resource_type/ART |
| dc.type.local.spa.fl_str_mv |
Artículo de investigación |
| format |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| status_str |
publishedVersion |
| dc.identifier.citation.spa.fl_str_mv |
Nagar, D. K., Bedoya-Valencia, D., & Gupta, A. K. (2015). Bivariate Generalization of the Gauss Hypergeometric Distribution. Applied Mathematical Sciences, 9(51), 2531-2551. http://dx.doi.org/10.12988/ams.2015.52111 |
| dc.identifier.issn.none.fl_str_mv |
1312-885X |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10495/26790 |
| dc.identifier.doi.none.fl_str_mv |
10.12988/ams.2015.52111 |
| dc.identifier.eissn.none.fl_str_mv |
1314-7552 |
| identifier_str_mv |
Nagar, D. K., Bedoya-Valencia, D., & Gupta, A. K. (2015). Bivariate Generalization of the Gauss Hypergeometric Distribution. Applied Mathematical Sciences, 9(51), 2531-2551. http://dx.doi.org/10.12988/ams.2015.52111 1312-885X 10.12988/ams.2015.52111 1314-7552 |
| url |
http://hdl.handle.net/10495/26790 |
| 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/ |
| dc.rights.accessrights.spa.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.creativecommons.spa.fl_str_mv |
https://creativecommons.org/licenses/by/4.0/ |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by/2.5/co/ http://purl.org/coar/access_right/c_abf2 https://creativecommons.org/licenses/by/4.0/ |
| dc.format.extent.spa.fl_str_mv |
21 |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| 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 |
| bitstream.url.fl_str_mv |
http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/2/license_rdf http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/3/license.txt http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/1/NagarDaya_2014_BivariateGaussDistribution.pdf |
| bitstream.checksum.fl_str_mv |
1646d1f6b96dbbbc38035efc9239ac9c 8a4605be74aa9ea9d79846c1fba20a33 e799f4d8ce73517d5a8cc7eb687bbafb |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad de Antioquia |
| repository.mail.fl_str_mv |
andres.perez@udea.edu.co |
| _version_ |
1812173207286841344 |
| spelling |
Nagar, Daya KrishnaBedoya Valencia, DaniloGupta, Arjun Kumar2022-03-22T21:24:23Z2022-03-22T21:24:23Z2014Nagar, D. K., Bedoya-Valencia, D., & Gupta, A. K. (2015). Bivariate Generalization of the Gauss Hypergeometric Distribution. Applied Mathematical Sciences, 9(51), 2531-2551. http://dx.doi.org/10.12988/ams.2015.521111312-885Xhttp://hdl.handle.net/10495/2679010.12988/ams.2015.521111314-7552ABSTRACT: The bivariate generalization of the Gauss hypergeometric distribution is defined by the probability density function proportional to x α1−1y α2−1 (1 − x − y) β−1 (1 + ξ1x + ξ2y) −γ , x > 0, y > 0, x + y < 1, where αi > 0, i = 1, 2, β > 0, −∞ < γ < ∞ and ξi > −1, i = 1, 2 are constants. In this article, we study several of its properties such as marginal and conditional distributions, joint moments and the coefficient of correlation. We compute the exact forms of R´enyi and Shannon entropies for this distribution. We also derive the distributions of X+Y , X/(X +Y ), V = X/Y and XY where X and Y follow a bivariate Gauss hypergeometric distribution.COL000053221application/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/Bivariate generalization of the Gauss hypergeometric distributionFuncionesFunctionsFunciones hipergeométricasHypergeometric functions62H1562E15Appl. Math. Sci.Applied Mathematical Sciences25312551951CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53ORIGINALNagarDaya_2014_BivariateGaussDistribution.pdfNagarDaya_2014_BivariateGaussDistribution.pdfArtículo de investigaciónapplication/pdf715904http://bibliotecadigital.udea.edu.co/bitstream/10495/26790/1/NagarDaya_2014_BivariateGaussDistribution.pdfe799f4d8ce73517d5a8cc7eb687bbafbMD5110495/26790oai:bibliotecadigital.udea.edu.co:10495/267902022-03-22 16:24:23.901Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |