Wind has become a popular renewable energy resource in the last two decades. Wind speed modeling is a crucial task for investors to estimate the energy potential of a region. The aim of this paper was to compare the popular unimodal wind speed distributions with their two-component mixture forms. Accordingly, Weibull, gamma, normal, lognormal distributions, and their two-component mixture forms; two-component mixture Weibull, two-component mixture gamma, two-component mixture normal, and two-component mixture lognormal distributions were employed to model wind speed datasets obtained from Belen Wind Power Plant and G??k?ßeada Meteorological Station. This paper also provides the comparison of gradient-based and gradient-free optimization algorithms for maximum likelihood (ML) estimators of the selected wind speed distributions. ML estimators of the distributions were obtained by using Newton--Raphson, Broyden--Fletcher--Goldfarb--Shanno, Nelder--Mead, and simulated annealing algorithms. Fit performances were compared based on Kolmogorov--Smirnov test, root mean square error, coefficient of determination ($R^2$), and power density error criteria. Results reveal that two-component mixture wind speed distributions have superiority over the unimodal wind speed distributions.