Abstract
In this paper we introduce the distribution of \(\frac{X_{1}^{c}}{X_{1}^{c}+X_{2}^{c}}\) , 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.
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Bekker, A., Roux, J. & Pham-Gia, T. The type I distribution of the ratio of independent “Weibullized” generalized beta-prime variables. Stat Papers 50, 323–338 (2009). https://doi.org/10.1007/s00362-007-0083-2
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DOI: https://doi.org/10.1007/s00362-007-0083-2
Keywords
- Gauss hypergeometric function
- Generalized beta-prime distribution
- Incomplete beta function
- Meijer’s G-function
- Predictive distribution
- Income distribution