We consider the random variables Z(i) = beta Y-2(i)i/Sigma(m)(k=1) beta Y-2(k)k where Y-i, i = 1..., m are independent inverted chi-square r.v. with nu(i) degrees of freedom. The probability density function of Z = (Z(1), Z(2), ...Z(m)) is obtained. When nu(i); i = 1..., m are odd, it is shown how to obtain in a fairly easy way a closed form expression for the expectation of log (Sigma(m)(k=1) beta Y-2(k)k). Differentiating this expression with respect to the beta(i), one can find the moments of the random variables Z(i). For the particular case of odd degrees of freedom, closed form expressions for the pdf of the univariate and multivariate marginal distributions of Z are also derived. The distribution of Z may be an alternative to the Dirichlet distribution for modeling compositional data.
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