MULTIVARIATE EXTREME-VALUE DISTRIBUTION WITH MIXED GUMBEL MARGINALS

Bivariate and trivariate distributions have been derived from the logi stic model for the multivariate extreme value distribution. Marginals in the models are extreme value type I distributions for two-component mixture variables (mixed Gumbel distribution). This paper is a contin uation of the previous works on multivariate distribution in hydrology . Interest is focused on the analysis of floods which are generated by different types of storms. The construction of their corresponding pr obability distributions and density functions are described. In order to obtain the parameters of such a bivariate or trivariate distributio n, a generalized maximum likelihood estimation procedure is proposed t o allow for the cases of samples with different lengths of record. A r egion in Northern Mexico with 42 gauging stations, grouped into two ho mogeneous regions, has been selected to apply the models. Results prod uced by the multivariate distributions have been compared with those o btained by the Normal, log-Normal-2, log-Normal-3, Gamma-2, Gamma-3, l og-Pearson-3, Gumbel, TCEV and General Extreme Value distributions. Go odness of fit is measured by the criterion of standard error of fit. R esults suggest that the proposed models are a suitable option to be co nsidered when performing flood frequency analysis.