Influence of the bandwidth in the harmonic search to optimize the mixed univariate Gumbel function

  • Juan Pablo Molina–AguilarEmail author
  • M. Alfonso Gutiérrez–López
Original Paper


Different regions of Mexico are affected temporarily by tropical cyclones whose evidence is reflected in the record of annual maximum flows of stream gages. The statistical analysis of these records presents two different trends represented by the Gumbel mixed distribution function. In order to achieve a reliable character of the historical information, it is necessary to determine the parameters of the function; therefore, the present work shows its optimization by means of the metaheuristic technique harmonic search verifying the influence of the bandwidth parameter in the solution. It was observed that the arithmetic expressions that define the bandwidth generate a better performance with respect to those that include exponential or logarithms. It is concluded that the technique achieves the optimization of the five parameters of the univariate Gumbel mixed function in an agile way, in particular the probability and the non-cyclonic elements, decreasing the adjustment error generated with respect to the classical methodologies, which improves upon having extensive historical records.



The authors thank Dr. Ramón Gerardo Guevara-Gonzalez for the comments and observations made in the revision of this article before submitting.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.División de Investigación y Posgrado, Facultad de IngenieríaUniversidad Autónoma de QuerétaroSantiago de QuerétaroMéxico
  2. 2.Centro de Investigaciones del Agua, Facultad de IngenieríaUniversidad Autónoma de QuerétaroSantiago de QuerétaroMéxico

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