## 1 Introduction  
As a common natural phenomenon, wind profoundly affects our lives. On the one hand, with the development of society and the global economy, humankind's demand for energy is increasing, and wind energy has been widely used as a clean energy in recent years [1, 2]. On the other hand, the volume of human buildings is gradually increasing, and more and more skyscrapers and large-span bridges have appeared, which are particularly sensitive to wind [3]. Whether it is for wind energy evaluation or structural wind resistance design, the study of wind characteristics is of fundamental importance. The most direct and effective way of studying wind characteristics is to measure them. For huge measured data, using the appropriate distribution model of wind speed and direction can simply and effectively describe its law. Many scholars have carried out extensive research on this. [PERSON] et al. [4] evaluated 115 different wind speed distribution models, as proposed in 46 articles from 2010 to 2018, according to the quantity and quality of analysis data; the results showed that five-parameter Wakeby distribution and four-parameter Kappa distribution scored the highest. [PERSON] et al. [5] proposed an innovative method, PWMBP (probability weighted moments based on the power density method), which was developed and proposed for estimating the Weibull parameters in wind energy applications. [PERSON] et al. [6] took four locations in central China as examples to compare commonly used wind speed probability distribution models and estimation methods of corresponding parameters. The results showed that the nonparametric model had better fitting accuracy and operation simplicity, and that the random heuristic algorithm was better than the widely used estimation method. [PERSON] et al. [7] compared the goodness of fit between 24 single-component probability density functions, 21 mixed probability density functions, and empirical wind speed probability density functionsworldwide. They found that the five-parameter Wakeby probability density function was suitable for land wind speed and the four-parameter Kappa probability density function was suitable for sea wind speed. The two-parameter Weibull probability density function is only optimal for a few wind speeds. [PERSON] et al. (2018) used the inverse Weibull (IW) distribution to model wind speed, and the results showed that, in most cases, IW distribution based on ML and MML parameter estimation had better results than Weibull distribution, based on corresponding estimation. [PERSON] et al. (2019) used generalized Lindley (GL) distribution and power Lindley (PL) distribution to model wind speed data. The results show that both GL distribution and PL distribution can provide the best fit according to different evaluation criteria. Many scholars have carried out research on the distribution of wind speed, but in many cases, wind direction also needs to be focused on; therefore, some scholars have conducted research on the distribution of wind direction and the joint distribution of wind direction and speed, through which the influence of wind direction can be considered. [PERSON] et al. (2019) used [PERSON] (vM-pdf) finite mixed distribution to represent the distribution of directional wind speed. Analysis of wind direction data from several weather stations in the Canary Islands shows that the model is suitable for wind conditions in areas with multiple patterns of prevailing wind directions. [PERSON] et al. (2019) predicted the basic wind speed of Sutong Bridge based on the joint distribution of wind speed and direction. [PERSON] et al. (2019) proposed extended parameter estimation algorithms for multivariate and multi-peak cyclic distribution to build a joint distribution model of wind speed and direction. It was found that the model had good representativeness, and that the algorithm could save significant amounts of time in parameter estimation. [PERSON] et al. (2019) proposed the use of non-parametric kernel density (NP-KD) and non-parametric JW (NP-JW) models.