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 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.

• 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/