  To assess the potential of wind energy in a specific area, statistical
distribution functions are commonly used to characterize wind speed
distributions. The selection of an appropriate wind speed model is crucial in
minimizing wind power estimation errors. In this paper, we propose a novel
method that utilizes the T-X family of continuous distributions to generate two
new wind speed distribution functions, which have not been previously explored
in the wind energy literature. These two statistical distributions, namely the
Weibull-three parameters-log-logistic (WE3-LL3) and log-logistic-three
parameters-Weibull (LL3-WE3) are compared with four other probability density
functions (PDFs) to analyze wind speed data collected in Tabriz, Iran. The
parameters of the considered distributions are estimated using maximum
likelihood estimators with the Nelder-Mead numerical method. The suitability of
the proposed distributions for the actual wind speed data is evaluated based on
criteria such as root mean square errors, coefficient of determination,
Kolmogorov-Smirnov test, and chi-square test. The analysis results indicate
that the LL3-WE3 distribution demonstrates generally superior performance in
capturing seasonal and annual wind speed data, except for summer, while the
WE3-LL3 distribution exhibits the best fit for summer. It is also observed that
both the LL3-WE3 and WE3-LL3 distributions effectively describe wind speed data
in terms of the wind power density error criterion. Overall, the LL3-WE3 and
WE3-LL3 models offer a highly accurate fit compared to other PDFs for
estimating wind energy potential.
