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Tecnología y ciencias del agua
On-line version ISSN 2007-2422
Abstract
CAMPOS-ARANDA, Daniel Francisco. Fit of the two-component extreme value (TCEV) distribution through of maximum likelihood. Tecnol. cienc. agua [online]. 2021, vol.12, n.2, pp.442-489. Epub June 26, 2025. ISSN 2007-2422. https://doi.org/10.24850/j-tyca-2021-02-10.
The annual record of floods, in many medium and large basins of our country and the world, is made up of events generated by phenomena which are physically different. For example, many floods originate from local storms, and a small portion is generated by cyclonic rains with a wide coverage and long duration, which generate extraordinary floods. The TCEV (two-component extreme value) distribution with four fitting parameters has been proposed for this type of records. TCEV has a theoretical basis that allows an approximate interpretation for two flood generation mechanisms, and it is also capable of reproducing the real variability of the asymmetry coefficient. This paper details its genesis and the fitting method by maximum likelihood, according to two numerical versions: (1) successive substitution and (2) objective function maximization. Six flood records were processed, the amplitude of which varied from 31 to 72 data, with three to six outliers or floods values that depart from the general trend. The predictions of the TCEV model, fitted with both numerical methods, are compared with those obtained using the standard application distributions (LP3, GVE and LOG) and the Wakeby distribution. Accepting the standard error of fit as a selection criterion, it follows that TCEV distribution is the best option in two of the six records processed. Lastly, as a conclusion, the systematic application of the TCEV distribution is suggested, using both numerical methods, in records with two mixed populations.
Keywords : TCEV distribution; Poisson process; maximum likelihood; Rosenbrock algorithm; standard error of fit; homogeneity and stationarity; prediction contrast.
