| Title | Exact and near-exact distributions of positive linear combinations of independent Gumbel random variables |
| Publication Type | Unpublished |
| Year of Publication | 2012 |
| Authors | Marques FJ, Coelho CA, de Carvalho M |
| Series Title | Preprint |
| Keywords | Generalized Integer Gamma distribution, Generalized Near-Integer Gamma distribution, Gumbel distribution, near-exact distributions |
| Abstract | We show that the exact distribution of a positive linear combination of independent Gumbel random variables can be written as the sum of a linear combination of independent log Gamma distributions, and an independent shifted Generalized Integer Gamma distribution. Given the complexity of this exact distribution, we develop a near-exact distribution using a shifted Generalized Near-Integer Gamma distribution. Our numerical studies confirm the quality of this near-exact approximation as assessed by a proximity measure often used in related studies. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/1_12.pdf |
