Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables
ABSTRACT: Let X and Y be independent random variables, X having a gamma distribution with shape parameter a and Y having a non-central gamma distribution with shape and non-centrality parameters b and δ, respectively. Define Z = X/(X + 2Y ). Then, the random variable Z has a non-central beta type 3...
- Autores:
-
Nagar, Daya Krishna
Ramírez Vanegas, Yeison Arley
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2013
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/31265
- Acceso en línea:
- https://hdl.handle.net/10495/31265
https://journaljamcs.com/index.php/JAMCS/article/view/22421
- Palabra clave:
- Variables aleatorias
Random variables
Análisis espectral
Spectrum analysis
Distribución de energía espectral
Spectral energy distribution
Funciones hipergeométricas
Functions, hypergeometric
Funciones de densidad
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
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Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| title |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| spellingShingle |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables Variables aleatorias Random variables Análisis espectral Spectrum analysis Distribución de energía espectral Spectral energy distribution Funciones hipergeométricas Functions, hypergeometric Funciones de densidad |
| title_short |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| title_full |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| title_fullStr |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| title_full_unstemmed |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| title_sort |
Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variables |
| dc.creator.fl_str_mv |
Nagar, Daya Krishna Ramírez Vanegas, Yeison Arley |
| dc.contributor.author.none.fl_str_mv |
Nagar, Daya Krishna Ramírez Vanegas, Yeison Arley |
| dc.contributor.researchgroup.spa.fl_str_mv |
Análisis Multivariado |
| dc.subject.lemb.none.fl_str_mv |
Variables aleatorias Random variables Análisis espectral Spectrum analysis Distribución de energía espectral Spectral energy distribution Funciones hipergeométricas Functions, hypergeometric |
| topic |
Variables aleatorias Random variables Análisis espectral Spectrum analysis Distribución de energía espectral Spectral energy distribution Funciones hipergeométricas Functions, hypergeometric Funciones de densidad |
| dc.subject.proposal.spa.fl_str_mv |
Funciones de densidad |
| description |
ABSTRACT: Let X and Y be independent random variables, X having a gamma distribution with shape parameter a and Y having a non-central gamma distribution with shape and non-centrality parameters b and δ, respectively. Define Z = X/(X + 2Y ). Then, the random variable Z has a non-central beta type 3 distribution, Z ∼ NCB3(a, b; δ). In this article we derive density functions of sum, difference, product and quotient of two independent random variables each having non central beta type 3 distribution. These density functions are expressed in series involving first hypergeometric function of Appell. |
| publishDate |
2013 |
| dc.date.issued.none.fl_str_mv |
2013 |
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2022-10-12T14:09:40Z |
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2022-10-12T14:09:40Z |
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Artículo de investigación |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Nagar, D. y Ramírez-Vanegas, Y. (2013). Distribuciones de Suma, Diferencia, Producto y Cociente de Variables Beta Tipo 3 No Centrales Independientes. Revista de Avances en Matemáticas e Informática , 3 (1), 12-23. https://doi.org/10.9734/BJMCS/2013/1895 |
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2231-0851 |
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https://hdl.handle.net/10495/31265 |
| dc.identifier.doi.none.fl_str_mv |
10.9734/BJMCS/2013/1895 |
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https://journaljamcs.com/index.php/JAMCS/article/view/22421 |
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Nagar, D. y Ramírez-Vanegas, Y. (2013). Distribuciones de Suma, Diferencia, Producto y Cociente de Variables Beta Tipo 3 No Centrales Independientes. Revista de Avances en Matemáticas e Informática , 3 (1), 12-23. https://doi.org/10.9734/BJMCS/2013/1895 2231-0851 10.9734/BJMCS/2013/1895 |
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https://hdl.handle.net/10495/31265 https://journaljamcs.com/index.php/JAMCS/article/view/22421 |
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eng |
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eng |
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23 |
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3 |
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12 |
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22 |
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British Journal of Mathematics & Computer Science |
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http://creativecommons.org/licenses/by/2.5/co/ |
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Sciencedomain International |
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India |
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Nagar, Daya KrishnaRamírez Vanegas, Yeison ArleyAnálisis Multivariado2022-10-12T14:09:40Z2022-10-12T14:09:40Z2013Nagar, D. y Ramírez-Vanegas, Y. (2013). Distribuciones de Suma, Diferencia, Producto y Cociente de Variables Beta Tipo 3 No Centrales Independientes. Revista de Avances en Matemáticas e Informática , 3 (1), 12-23. https://doi.org/10.9734/BJMCS/2013/18952231-0851https://hdl.handle.net/10495/3126510.9734/BJMCS/2013/1895https://journaljamcs.com/index.php/JAMCS/article/view/22421ABSTRACT: Let X and Y be independent random variables, X having a gamma distribution with shape parameter a and Y having a non-central gamma distribution with shape and non-centrality parameters b and δ, respectively. Define Z = X/(X + 2Y ). Then, the random variable Z has a non-central beta type 3 distribution, Z ∼ NCB3(a, b; δ). In this article we derive density functions of sum, difference, product and quotient of two independent random variables each having non central beta type 3 distribution. These density functions are expressed in series involving first hypergeometric function of Appell.COL000053212application/pdfengSciencedomain InternationalIndiahttp://creativecommons.org/licenses/by/2.5/co/https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Distributions of sum, difference, product and quotient of independent noncentral beta type 3 variablesArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionVariables aleatoriasRandom variablesAnálisis espectralSpectrum analysisDistribución de energía espectralSpectral energy distributionFunciones hipergeométricasFunctions, hypergeometricFunciones de densidad2331222British Journal of Mathematics & Computer SciencePublicationLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstreams/f7fb7357-0c85-40af-94da-4e986e924c92/download8a4605be74aa9ea9d79846c1fba20a33MD53falseAnonymousREADORIGINALNagarDaya_2013_Distributions-Sum.pdfNagarDaya_2013_Distributions-Sum.pdfArtículo de investigaciónapplication/pdf357159https://bibliotecadigital.udea.edu.co/bitstreams/85b02303-65d0-4c55-ab6b-bcae5d519f33/download5352f6d586c622189888fc5b36e7a968MD51trueAnonymousREADCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstreams/41fa4c4a-1e9e-4714-915b-bd8965e05362/download1646d1f6b96dbbbc38035efc9239ac9cMD52falseAnonymousREADTEXTNagarDaya_2013_Distributions-Sum.pdf.txtNagarDaya_2013_Distributions-Sum.pdf.txtExtracted texttext/plain26609https://bibliotecadigital.udea.edu.co/bitstreams/a018dbe7-6aa3-4197-ac9b-b008494b937c/downloadd4b872456f2631c374d1b3906ee118eaMD54falseAnonymousREADTHUMBNAILNagarDaya_2013_Distributions-Sum.pdf.jpgNagarDaya_2013_Distributions-Sum.pdf.jpgGenerated Thumbnailimage/jpeg11475https://bibliotecadigital.udea.edu.co/bitstreams/ade193eb-b100-4414-a4bf-b264c97d63ee/download6f85efd0f0deff962149cbff6a7bc5a4MD55falseAnonymousREAD10495/31265oai:bibliotecadigital.udea.edu.co:10495/312652025-03-27 00:28:54.375http://creativecommons.org/licenses/by/2.5/co/open.accesshttps://bibliotecadigital.udea.edu.coRepositorio Institucional de la Universidad de Antioquiaaplicacionbibliotecadigitalbiblioteca@udea.edu.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 |