  Wind speed statistics is generally modeled using the Weibull distribution.
This distribution is convenient since it fully characterizes analytically with
only two parameters (the shape and scale parameters) the shape of distribution
and the different moments of the wind speed (mean, standard deviation, skewness
and kurtosis). This distribution is broadly used in the wind energy sector to
produce maps of wind energy potential. However, the Weibull distribution is
based on empirical rather than physical justification and might display strong
limitations for its applications. The philosophy of this article is based on
the modeling of the wind components instead of the wind speed itself. This
provides more physical insights on the validity domain of the Weibull
distribution as a possible relevant model for wind statistics and the
quantification of the error made by using such a distribution. We thereby
propose alternative expressions of more suited wind speed distribution.
