Contrast of frequency analysis between beta-kappa and beta-Pareto distributions with three of widespread application; [Contraste de análisis de frecuencias entre las distribuciones beta-kappa y beta-Pareto con tres de aplicación generalizada]
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abstract
The hydrological design of several hydraulic works or the revision of the constructed ones is based on the design floods, which are maximum flows of the river, associated with low probabilities of exceedance or predictions. Its most reliable estimate is made through frequency analysis, statistical process that consists of representing the record of maximum annual flows, with a probability distribution function (PDF) or probabilistic model, used to make the desired predictions. In this contrast study, the beta-kappa and beta-Pareto FDPs are proposed, and the following three were considered to be widely used FDPs: Log-Pearson type III, general extreme values, and generalized logistics. Therefore, it is exposed, for the first two FDP, a summary of his theory and his method of fit for maximum likelihood is presented. Eleven annual extreme hydrological data records are processed and the fits are contrasted with two indices: The standard error of fit and the mean absolute error. The selection of the predictions in the seven return periods (Tr) studied was based on the lower values of the fit errors and on the search for representative predictions in the Tr ≥ 500 years. The conclusions suggest the inclusion of the beta-kappa and beta-Pareto distributions in the frequency analysis due to their versatility and fit facility.
Beta-kappa distribution; beta-Pareto distribution; maximum likelihood fit; mean absolute error; predictions; Q-Q graphics; standard error of fit error correction; frequency analysis; probability; standard (reference)
