The Gumbel Mixed Model Applied to Storm Frequency Analysis

By S. Yue. 2000

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On the construction of multivariate extreme value models via copulas (2009, methodology): “This copula represents a sort of “standard” MEV model in hydrology (see, e.g., Yue, 2000a,b, and references therein); in particular, it is the only Archimedean copula that is also MEV (Genest and Rivest, 1989).”
Multivariate multiparameter extreme value models and return periods: A copula approach (2010, background): “…the multivariate lognormal’s, Student’s t and Fisher’s F distributions [see, e.g., Alexander, 1954; Stedinger, 1983; Hosking and Wallis, 1988; Pons, 1992; Kottegoda and Natale, 1994]), or multivariate logistic Gumbel [see, e.g., Raynal‐Villasenor and Salas, 1987; Bacchi et al., 1994; Yue, 2000b].”
Design hyetograph analysis with 3-copula function (2006, methodology): “This approach was re-proposed by Yue (2000a) introducing the optimization of the likelihood function to assess the parameters of the Box-Cox transformation.”
Statistics of Extremes (2004, methodology): “16), despite the abundance of ad hoc methods for statistical inference on ψ (Gumbel and Mustafi 1967; Posner et al. 1969; Tiago de Oliveira 1980, 1989b; Yue 2000; Yue et al. 1999), maximum likelihood estimation is the most efficient.”