Fit of the two-component extreme value (TCEV) distribution through of maximum likelihood

Abstract

The annual record of floods, in many medium and large basins of our country and the world, is made up of events generated by physically different phenomena. For example, many floods originate from local storms and a small portion is generated by cyclonic rains of wide coverage and duration, which generate extraordinary floods. The TCEV distribution (two-component extreme value) with four fitting parameters has been proposed for this type of records. TCEV has a theoretical basis that allows an approximate interpretation for two mechanisms of generation of the floods 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 registries of floods 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 the TCEV distribution is the best option in two of the six processed records. Lastly, as conclusion, the systematic application of the TCEV distribution is suggested, using both numerical methods, in records that present two mixed populations.