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| Título | On the distribution of the product and ratio of independent central and doubly non-central Generalized Gamma Ratio random variables |
| Publication Type | Unpublished |
| Year of Publication | 2005 |
| Authors | Coelho CA, Mexia JT |
| Series Title | Preprint |
| Abstract | Using a decomposition of the characteristic function of the logarithm of the product of independent Generalized Gamma Ratio random variables we obtain explicit expressions for both the probability density and cumulative distribution functions of the product of independent central or non-central random variables with generalized F or Generalized Gamma Ratio distributions under the form of particular mixtures of Pareto and inverted Pareto distributions. The expressions obtained do not involve any unsolved integrals and are much adequate for computer implementation and the development of asymptotic and near-exact distributions. By considering not necessarily positive power parameters we were able to obtain as particular cases not only the product of Beta prime, folded T, folded Cauchy and F random variables but also the densities and distributions for the ratio of two independent Generalized Gamma Ratio random variables or two independent products of such variables. Products of Generalized Gamma Ratio distributions may be applied in the study of multivariate linear functional models. As a by-product we also obtain closed form representations for the distribution of the difference of two independent sums of a finite number of Gamma random variables with different rate parameters and integer shape parameters, under the form of finite mixtures of Gamma distributions, as well as the distributions for the product and ratio of generalized Pareto distributions, under the form of finite mixtures of Pareto and inverted Pareto distributions. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2005/11_05.pdf |