# Weibull and Generalized Extreme Value Distributions for Wind Speed Data Analysis of Some Locations in India

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## Abstract

Wind velocity data modeling plays a crucial role for the estimation of wind load and wind energy. Apart from these, the same modeling must also be used in the load cycle analysis of fatigue failure in slender structures to address periodic vortex shedding. Most authors fitted the entire available range of wind velocities of various locations using Weibull models. However, they did not check the validity of the model in describing the range of extreme wind velocity. In this work, the validity of Weibull models for describing parent as well as extreme hourly mean wind velocity data for four places on the east coast of India has been checked. While it predicts lower wind speeds accurately, the Weibull model has been found to become inappropriate for describing wind velocity in the range of extremes, i.e., above a certain threshold value. Therefore, this article focuses on the techniques of determining a limiting wind velocity beyond which the Weibull distribution is rendered unsuitable. In the range where the Weibull distribution fails, various extreme value distributions, such as Gumbel, Fréchet and reverse Weibull distributions have been compared, thereby determining the best estimator for each location.

## Keywords

weibull distribution wind velocities non-exceedance probability gumbel distribution chauvenet’s criterion probability factor## Preview

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## Notes

### Acknowledgments

The authors are grateful to the Indian Meteorological Department, Pune, for supplying wind velocity data. The corresponding author would like to thank professor Michael Kasperski for encouraging him to conduct research in wind climatology during his DAADsupported stay in Germany. The authors would like to thank BRNS, Department of Atomic Energy, Govt. of India for providing financial support for this research via Grant No. 2012/36/65-BRNS. The authors would also like to acknowledge Ms. Debanshee Datta, SRF and Mr. Ahin Banerjee, JRF for providing necessary help and logistic support. They are also obliged to Dr. Arabin Kumar Dey, Associate Professor, Department of Mathematics, IIT, Guwahati for helping them to reply reviewers’ comments.

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