Fitting of the Log-Pearson Type III Distribution through Unconstrained Numerical Optimization

Abstract

Firstly, the importance of flood frequency analysis (FFA) is pointed out when design flows are estimated and hydrometric information is available. Log-Pearson type distribution (LP3) has been established as a basic model of the FFA. Now, in this work, the fitting of that distribution is proposed for the available sample by unconstrained numerical optimization, using the Rosenbrock algorithm to minimize the non-linear objective function given by the quadratic mean error and the absolute mean error. Three variables to be optimized are considered: the mean, the standard deviation, and the skew coefficient of the natural logarithms of data. The results of the indirect moments method are taken as initial values. It was found that the suggested procedure always improves the best LP3 distribution fittings in the 31 records of annual maximum events. These fiitings were previously tested with six methods. Moreover, a test through simulation was made between the indirect moments method and the one proposed, using synthetic sequences, which proved that the secondprocedure was better. On the other hand, there is a great similarity in the magnitude of the predictions obtained with the other methods and with the one proposed; these predictions are associated to seven return periods, which varied from 10 to 10,000 years. The above allows a more objective and reliable selection of the searched predictions.