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Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

1
Division de Investigacion y Posgrado, Facultad de Ingenieria, Universidad Autonoma de Queretaro, Cerro de las Campanas S/N. Col. Niños Heroes, Santiago de Queretaro C.P. 76010, Queretaro, Mexico
2
Centro de Investigaciones del Agua. Facultad de Ingenieria, Universidad Autonoma de Queretaro, Cerro de las Campanas S/N. Col. Niños Heroes, Santiago de Queretaro C.P. 76010, Queretaro, Mexico
3
Escuela de Ingenieria, Universidad de las Americas Puebla. Sta. Catarina Martir. San Andres Cholula C.P. 72810, Puebla, Mexico
4
Casas Ponty, Ignacio Zaragoza Pte. 280. Col. Niños Heroes, Santiago de Queretaro C.P. 76010, Queretaro, Mexico
*
Author to whom correspondence should be addressed.
Atmosphere 2019, 10(5), 257; https://doi.org/10.3390/atmos10050257
Received: 18 March 2019 / Revised: 13 April 2019 / Accepted: 17 April 2019 / Published: 9 May 2019
(This article belongs to the Special Issue Weather and Climate Extremes: Current Developments)
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Abstract

Due to its geographical position, Mexico is exposed annually to cold fronts and tropical cyclones, registering extremely high values that are atypical in the series of maximum annual flows. Univariate mixed probability distribution functions have been developed based on the theory of extreme values, which require techniques to determine their parameters. Therefore, this paper explores a function that considers three populations to analyze maximum annual flows. According to the structure of the Generalized Extreme-Value Distribution (GEV), the simultaneous definition of nine parameters is required: three of location, three of scale, and three of probability of occurrence. Thus, the use of a meta-heuristic technique was proposed (harmonic search). The precision of the adjustment was increased through the optimization of the parameters, and with it came a reduction in the uncertainty of the forecast, particularly for cyclonic events. It is concluded that the use of an extreme value distribution (Type I) structured with three populations and accompanied by the technique of harmonic search improves the performance in respect to classic techniques for the determination of its parameters. View Full-Text
Keywords: harmonic search; Generalized Extreme-Value Distribution (GEV); maximum annual flow; flow frequency analysis; mixed Gumbel; three populations Gumbel distribution; EV1 harmonic search; Generalized Extreme-Value Distribution (GEV); maximum annual flow; flow frequency analysis; mixed Gumbel; three populations Gumbel distribution; EV1
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Molina-Aguilar, J.P.; Gutierrez-Lopez, A.; Raynal-Villaseñor, J.A.; Garcia-Valenzuela, L.G. Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search. Atmosphere 2019, 10, 257.

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