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MULTIVARIATE EXTREME VALUE DISTRIBUTION WITH MIXED GUMBEL MARGINALS 1
Author(s) -
EscalanteSandoual Carlos
Publication year - 1998
Publication title -
jawra journal of the american water resources association
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.957
H-Index - 105
eISSN - 1752-1688
pISSN - 1093-474X
DOI - 10.1111/j.1752-1688.1998.tb04138.x
Subject(s) - gumbel distribution , generalized extreme value distribution , mathematics , extreme value theory , statistics , multivariate statistics , multivariate stable distribution , bivariate analysis , normal wishart distribution , multivariate normal distribution , gamma distribution
Bivariate and trivariate distributions have been derived from the logistic 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 continuation 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 probability distributions and density functions are described. In order to obtain the parameters of such a bivariate or trivariate distribution, a generalized maximum likelihood estimation procedure is proposed to allow for the cases of samples with different lengths of record. A region in Northern Mexico with 42 gauging stations, grouped into two homogeneous regions, has been selected to apply the models. Results produced by the multivariate distributions have been compared with those obtained by the Normal, log‐Normal‐2, log‐Normal‐3, Gamma‐2, Gamma‐3, log‐Pearson‐3, Gumbel, TCEV and General Extreme Value distributions. Goodness of fit is measured by the criterion of standard error of fit. Results suggest that the proposed models are a suitable option to be considered when performing flood frequency analysis.