Modelling wind speed with a univariate probability distribution depending on two baseline functions

Characterizing the wind speed distribution properly is essential for the satisfactory pro-duction of potential energy in wind farms, being the mixture models usually employed in the description of such data. However, some mixture models commonly have the unde-sirable property of non-identifiability. In this work, we present an alternative distribution which is able to fit the wind speed data decently. The new model, called Normal-Weibull-Weibull, is identifiable and its cumulative distribution function is written as a composition of two baseline functions. We discuss structural properties of the class that generates the proposed model, such as the linear representation of the probability density function, mo-ments and moment generating function. We perform a Monte Carlo simulation study to investigate the behavior of the maximum likelihood estimates of the parameters. Finally, we present applications of the new distribution for modelling wind speed data measured in five different cities of the Northeastern Region of Brazil.

Automated summary

Characterizing the wind speed distribution is crucial for wind farms' energy production, but existing mixture models often suffer from the undesirable property of non-identifiability. In this study, we propose a new identifiable distribution model, the Normal-Weibull-Weibull, which can fit wind speed data effectively. We discuss the structural properties of the model class and perform a Monte Carlo simulation study to analyze the behavior of the parameter estimates. Finally, we apply the new distribution model to wind speed data from five cities in the Northeastern Region of Brazil.