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| Título | On the product of independent Generalized Gamma random variables |
| Publication Type | Unpublished |
| Year of Publication | 2012 |
| Authors | Marques FJ |
| Series Title | Preprint |
| Palavras-chave | asymptotic approximation, characteristic function, Gamma distribution, Generalized Integer Gamma distribution, Generalized Near-Integer Gamma distribution, logGamma distribution, near-exact distributions. |
| Abstract | The product of independent Generalized Gamma random variables arises in many problems and applications of the most different areas. Working with characteristic functions, which are the Fourier transforms of density functions, we study the structure of the exact distribution and, based on a truncation of the characteristic function of the negative logarithm of the product of independent Generalized Gamma random variables, a simple and accurate near-exact distribution is developed. The density and cumulative distribution functions of the near-exact distribution have manageable expressions allowing for the computation of p-values and quantiles. In the process, a flexible parameter, gamma, is introduced in the representations of the exact and near-exact distributions which allows to choose the quality of the approximation developed. The numerical studies and simulations carried out show the accuracy of this approximation as well as its asymptotic properties. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/14_12.pdf |