%0 Journal Article
%T BIVARIATE GENERALIZATION OF THE KUMMER-BETA DISTRIBUTION GENERALIZACI車N BIVARIADA DE LA DISTRIBUCI車N KUMMER-BETA
%A Bran-Cardona Paula Andrea
%A Orozco-Castaˋeda Johanna Marcela
%A Nagar Daya Krishna
%J Revista Colombiana de Estad赤stica
%D 2011
%I Universidad Nacional de Colombia
%X In this article, we study several properties such as marginal and conditional distributions, joint moments, and mixture representation of the bivariate generalization of the Kummer-Beta distribution. To show the behavior of the density function, we give some graphs of the density for different values of the parameters. Finally, we derive the exact and approximate distribution of the product of two random variables which are distributed jointly asbivariate Kummer-Beta. The exact distribution of the product is derived as an infinite series involving Gauss hypergeometric function, whereas the beta distribution has been used as an approximate distribution. Further, to show the closeness of the approximation, we have compared the exact distribution and the approximate distribution by using several graphs. An application of the results derived in this article is provided to visibility data from Colombia. En este art赤culo, definimos la funci車n de densidad de la generalizaci車n bivariada de la distribuci車n Kummer-Beta. Estudiamos algunas de sus propiedades y casos particulares, as赤 como las distribuciones marginales y condicionales. Para ilustrar el comportamiento de la funci車n de densidad, mostramos algunos gr芍ficos para diferentes valores de los par芍metros. Finalmente, encontramos la distribuci車n del producto de dos variables cuya distribuci車n conjunta es Kummer-Beta bivariada y utilizamos la distribuci車n beta como una aproximaci車n. Adem芍s, con el fin de comparar la distribuci車n exacta y la aproximada de este producto, mostramos algunos gr芍ficos. Se presenta una aplicaci車n a datos clim芍ticos sobre niebla y neblina de Colombia.
%K Beta distribution
%K Bivariate distribution
%K Dirichlet distribution
%K Hypergeometric function
%K Moments
%K Transformation
%U http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512011000300007