Abstract
We consider the random variables where are independent inverted chi-square r.v. with νi degrees of freedom. The probability density function of is obtained. When are odd, it is shown how to obtain in a fairly easy way a closed form expression for the expectation of Differentiating this expression with respect to the βi, one can find the moments of the random variables Zi. 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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