This paper presents a comprehensive empirical study of five distribution functions to analyze wind energy potential: Rayleigh, Weibull, Gamma, Burr Type XII, and Generalized Extreme Value. In addition, two metaheuristics optimization methods, Grey Wolf optimization and Whale optimization algorithm, are utilized to determine the optimal parameter values of each distribution. Five error measures are investigated and compared to test the accuracy of the introduced distributions and optimization methods, such as mean absolute error, root mean square error, regression coefficient, correlation coefficient, and net fitness. The Catalca site in Istanbul, Turkey, was selected to be the case study to conduct this analysis. The obtained results confirm that all introduced distributions based on optimization methods efficiently model wind speed distribution in the selected site. Although Gamma distribution based on GWO and WOA outperformed other distributions for all datasets at all heights, it was the worst in terms of computation complexity. Rayleigh distribution occupied the latest rank, but it was the best in terms of computation complexity. MATLAB 2020b and Excel 365 were used to perform this study.