Non linear discriminant based on mixture of distributions: an application in return time of heterogeneous maximum flows observed in the Paranapanema river basin-Brazil

Authors

DOI:

https://doi.org/10.17268/sel.mat.2020.02.06

Keywords:

MGEV, Discriminant Analysis, Flows, Return Period

Abstract

In this work, maximum flows observed in the Paranapanema river basin are modeled by a mixture of two GEV distributions whose components correspond to the summer and winter subpopulations. The nonlinear discriminant function allowed to confirm the assumption of mixture model.The proposed model is then used to determine probabilities of exceedance and return periods associated with extreme flows, which are of fundamental importance for hydraulic projects. The results show significant differences when a mixture model is used and therefore an approach more coherent with the observed data.

References

Ahmad KE, Abd-Elrahman AM. Updating a nonlinear discriminant function estimated from a mixture of two Weibull distributions. Math. Comput. Modelling. 1994; 19(11):41–51.

Ahmad KE, Jaheen ZF, Modhesh AA. Estimation of a discriminant function based on small sample size from a mixture of two Gumbel distributions. Comm. Statist. Simulation Comput. 2010; 39(4):13–725.

Alila Y, Mtiraoui A. Implications of heterogeneous flood-frequency distributions on traditional stream-discharge prediction techniques. Hydrological Process. 2002; 16:1065–1084.

Amoh RK. Estimation of a discriminant function from a mixture of two inverse Gaussian distributions when the sample size is small. J. Statist. Comp. Simul. 1985; 20:275–286.

Cruvinel EC. Discriminante para mistura de distribuicoes GEV.[ Dissertacao de Mestrado]. Brasilia: Universidade de Brasília. 2017. Disponivel en: http://repositorio.unb.br/handle/10482/24006.

Escalante-Sandoval C. A Mixed distribution with EV1 and GEV components for analyzing heterogeneous samples. Ingeniería, investigación y tecnología. 2007; 8(3):1405-7743.

Girardo G. Volume de chuvas em fevereiro em Sao Paulo já é maior desde 1999[Intenet]. Sao Paulo: O Estado de S. Paulo; 2020[ Consultado em 09 dezembro de 2020]. Recuperado de https://sao-paulo.estadao.com.br/noticias/geral,volume-dechuvas-em-fevereiro-em-sp-ja-e-o-maior-desde-1999,70003194244.

Fiorentino M, Arora K, Singh VP. The two-component extreme value distribution for flood frequency analysis: Derivation of a new estimation method. Stochastic Hydrology and Hydraulics. 1987; 1(3):199–208.

Jenkinson AF. The frequency distribution of anual maximum (or minimum) values of metereological elements. Quarterly J. of the Royal Met. Society. 1995; 8:145–158.

McLachlan GJ, Peel D. Finite Mixture Models. Australia: John Wiley, 2004.

Otiniano CEG, Teixeira ECM. Estimacao dos parámetros da mistura de duas componentes GEV via Algoritmo EM. Tendencias em Matemática Aplicada e Computacional. 2014; 15(1):59–71.

Rossi F, Fiorentino M, Versace P. Two-component extreme value distribution for flood frequency analysis. Water Resour. Res. 1994; 20(7):847–856.

Sultan KS, Al-Moisheer AS. Estimation of a discriminant function from a mixture of two inverse weibull distributions. J. of Statistical Computation and Simulation. 2013; 83(3):405–416.

Singh KP. Hydrologic distributions resulting from mixed populations and their computer simulations. I.A.S.H. 1968; 8:671–681.

Downloads

Published

2020-12-25

How to Cite

Guevara Otiniano, C. E., C. Cruvinel, E., & H. Lima, C. (2020). Non linear discriminant based on mixture of distributions: an application in return time of heterogeneous maximum flows observed in the Paranapanema river basin-Brazil. Selecciones Matemáticas, 7(02), 242-249. https://doi.org/10.17268/sel.mat.2020.02.06

Issue

Vol. 7 No. 02 (2020): August - December

Section

Articles

License

The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.