Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation

Elio Chiodo; Pasquale De Falco; Luigi Pio Di Noia; Fabio Mottola; Elio Chiodo; Pasquale De Falco; Luigi Pio Di Noia; Fabio Mottola

doi:10.3934/energy.2018.6.926

AIMS Energy

2018, Volume 6, Issue 6: 926-948. doi: 10.3934/energy.2018.6.926

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Research article Topical Sections

Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation

1.
Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
2.
Department of Engineering, University of Naples Parthenope, Naples, Italy
3.
Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, Italy

Received: 03 August 2018 Accepted: 18 October 2018 Published: 29 October 2018

Extreme Wind Speed modeling, i.e. the probabilistic characterization of extreme values of wind speed, is a key tool for properly understanding the destructive wind forces which may affect mechanical safety and reliability of wind power systems, but it is also extremely useful for the purpose of achieving accurate wind energy production estimations. Indeed, the need of more accurate wind estimations has been often highlighted in the literature, especially for Extreme Wind Speed, since classical adopted models, such as the Weibull distribution, behave poorly in the range of Extreme Wind Speed values. In the paper, a new model, generated by a proper mixture of the established Inverse Weibull distribution, is proposed and illustrated. The proposal is the “Inverse Log-logistic” distribution, whose adequacy in interpreting some sets of real Extreme Wind Speed data is shown after giving some hints to its identification. This study also develops a peculiar Bayesian statistical inference approach for the estimation of the above model from available data, using different prior distributions, i.e. the Lognormal, the Generalized Gamma and the Uniform distribution. Extensive numerical simulations confirm that the proposed estimation technique constitutes a very fast, efficient and robust method for the Extreme Wind Speed modeling.
- Bayes estimation,
- Extreme Wind Speed,
- Inverse Log-logistic distribution,
- Inverse Weibull distribution,
- probability,
- renewable energy
Citation: Elio Chiodo, Pasquale De Falco, Luigi Pio Di Noia, Fabio Mottola. Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation[J]. AIMS Energy, 2018, 6(6): 926-948. doi: 10.3934/energy.2018.6.926

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Abstract

Extreme Wind Speed modeling, i.e. the probabilistic characterization of extreme values of wind speed, is a key tool for properly understanding the destructive wind forces which may affect mechanical safety and reliability of wind power systems, but it is also extremely useful for the purpose of achieving accurate wind energy production estimations. Indeed, the need of more accurate wind estimations has been often highlighted in the literature, especially for Extreme Wind Speed, since classical adopted models, such as the Weibull distribution, behave poorly in the range of Extreme Wind Speed values. In the paper, a new model, generated by a proper mixture of the established Inverse Weibull distribution, is proposed and illustrated. The proposal is the “Inverse Log-logistic” distribution, whose adequacy in interpreting some sets of real Extreme Wind Speed data is shown after giving some hints to its identification. This study also develops a peculiar Bayesian statistical inference approach for the estimation of the above model from available data, using different prior distributions, i.e. the Lognormal, the Generalized Gamma and the Uniform distribution. Extensive numerical simulations confirm that the proposed estimation technique constitutes a very fast, efficient and robust method for the Extreme Wind Speed modeling.

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