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/
| Summary: | 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. |
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