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

TL;DR

This paper introduces the Normal-Weibull-Weibull distribution, an identifiable univariate model based on two baseline functions, for accurately characterizing wind speed data, addressing issues of non-identifiability in traditional mixture models.

Contribution

The paper proposes a novel identifiable distribution for wind speed modeling, with a composition of two baseline functions, and explores its properties and practical applications.

Findings

The new model fits wind speed data effectively across five Brazilian cities.

Monte Carlo simulations validate the reliability of maximum likelihood estimates.

The distribution's structural properties facilitate understanding of wind speed behavior.

Abstract

Characterizing the wind speed distribution properly is essential for the satisfactory production 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 undesirable property of non-identifiability. In this work, we present an alternative distribution which is able to fit the wind speed data adequately. 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, moments 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.