The type I distribution of the ratio of independent 'Weibullized' generalized beta-prime variables

摘要

In this paper we introduce the distribution of X-1(c)/X-1(c)+X-2(c), with c>0, where X-i, i = 1, 2, are independent generalized beta-prime-distributed random variables, and establish a closed form expression of its density. This distribution has as its limiting case the generalized beta type I distribution recently introduced by Nadarajah and Kotz ( 2004). Due to the presence of several parameters the density can take a wide variety of shapes.