## 1 Introduction  
The wind speed is extremely variable; at a given location it varies with time and height while also depending on the shape and roughness of the terrain (surrounding landscape, vegetation, and structures). The wind speed decreases with a rougher surface, but it can accelerate on steep hills, reaching its maximum at the crest and then splitting into zones of turbulent air flow. Its fluctuating nature requires appropriate means for its description, and right here the probability distributions can provide a useful tool in modelling the wind speed. Wind speed modelling via probability distributions, which is based on long-term observations, is relatively stable and based on long-term statistical characteristics of wind [1, 2]. Because strong winds are known to be rare, whilst mild and fresh winds are more common, the probability distributions more suitable for wind speed modelling are those skewed to the right. The two-parameter Weibull distribution is often presented as the first choice for modelling many wind sites since it can provide a good agreement with the experimental data [3]. This probability distribution has many advantages, such as a simple form, high flexibility, the probability density function and the cumulative distribution function are described in a closed form, and a relatively simple estimation of the parameters. It was first introduced by the Swedish scientist [PERSON] (1887-1979), who used it in the theory of reliability. The Weibull distribution appears to be a powerful tool for statistical analysis of data in many areas, such as engineering, materials science, quality, physics, medicine, meteorology, and hydrology. The use of the Weibull distribution to describe the wind speed has a long history. This distribution was first applied to wind speed data by [PERSON] in [4]. Since then, it has been successfully used for modelling the wind speed in many sites, for example, in India [5], Pakistan [6; 7], South Korea [8], West Africa [9], U.S.A. [10], Cook Islands [11], Palestine [12], Iraq [13], Nigeria [14], United Kingdom [15], Austria [16], Slovakia [17], and many more. Therefore, the Weibull distribution is commonly used as a wind speed distribution and is implemented in many commercial programs [18]. However, the two-parameter Weibull distribution is not universal and it does not suit all the existing wind regimes [19]. As previous studies have shown, the two-parameter Weibull distribution is less effective in fitting low wind speeds, especially when the probability of null wind is significant--null wind speed data needs to be removed before fitting, making it impossible to characterise some of the existing wind regimes [18; 20]. As an alternative to the two-parameter Weibull distribution, the three-parameter Weibull distribution has also been used in some studies, and it has been found to provide a greater flexibility than the classical two-parameter Weibull function [21; 22]. It proved to better fit the wind speed (compared to the two-parameter Weibull function) when there is a higher frequency of lower values of wind speed, including null wind [18]. This has motivated authors to successfully apply other known probability distributions, for example, Extreme Value [23], Gamma [24], Gumbel [25], Nakagami [26], Birnbaum-Saunders [27], Wakeby and Kappa [28], Lindley [29], and many more. Furthermore, it propelled many authors to search for more flexible and better fitting probability distributions using generalizations of classical probability distributions. Several methods to improve the flexibility by adding one or more parameters to the distributions have been proposed and such generalizations have been made through different approaches [30]: the transformation method [31; 32], the composition of two or more distributions, the compounding of distributions, and the mixture of classical distributions [33; 34; 35; 36; 37].