A Trivariate Extreme Value Distribution Applied to Flood Frequency Analysis

A trivariate extreme value distribution has been derived from the logistic model for the multivariate extreme value distribution. The construction of its corresponding probability distribution and density function is described. In order to obtain the parameters of such a trivariate distribution, a generalized maximum likelihood estimation procedure is described to allow for the cases of samples with different record lengths. Furthermore the reliability of the estimated parameters of the irivariate extreme value distribution is measured through the use of relative information ratios. A region in Northern Mexico with six gauging stations has been selected to apply the trivariate model. Results produced by the proposed model have been compared with those obtained by general extreme value (GEV) distribution functions.