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

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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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Authors and Affiliations

  1. Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, 0002, South Africa

    Andriëtte Bekker & Jacobus Roux

  2. Department of Mathematics and Statistics, Université de Moncton, Moncton, NB, E1A 3EO, Canada

    Thu Pham-Gia

Authors
  1. Andriëtte Bekker
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  2. Jacobus Roux
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  3. Thu Pham-Gia
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Correspondence to Andriëtte Bekker.

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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

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