Modeling wind energy flux by a Birnbaum–Saunders distribution with an unknown shift parameter

Abstract

In this paper, we discuss a Birnbaum–Saunders distribution with an unknown shift parameter and apply it to wind energy modeling. We describe structural aspects of this distribution including properties, moments, mode and hazard and shape analyses. We also discuss estimation, goodness of fit and diagnostic methods for this distribution. A computational implementation in R language of the obtained results is provided. Finally, we apply such results to two unpublished real wind speed data from Chile, which allows us to show the characteristics of this statistical distribution and to model wind energy flux.

Keywords:

• diagnostic and goodness-of-fit techniques
• hazard analysis
• ML methods
• moments
• wind speed

Acknowledgements

The authors would like to thank the Editor-in-Chief Professor Robert Aykroyd and three anonymous referees for their helpful comments aided in improving this article. This study was developed during a stay of two months of Dr. Víctor Leiva in the Department of Mathematics and Applications and the Centre of Mathematics (CMat) of the Universidade do Minho in Braga, Portugal. Dr. Leiva wishes to specially thank the Universidade do Minho and colleagues and staff of this Department for the support and hospitality during this stay. This study was supported by the CMat through the FCT Pluriannual Funding Program, Portugal, and by the FONDECYT 1080326 grant, Chile.