Critical evaluation of wind speed frequency distribution functions

Over the past few years a number of new mathematical functions have been proposed for wind speed probability density distributions. The most commonly used function that has been cited in literature has been the two-parameter Weibull function. However, in recent years studies have shown that the two-parameter Weibull function might be inadequate in modeling the wind speed probability density distributions or independent of whether the distribution is of unimodal or bimodal nature. For the unimodal distributions, the inadequacy may be due to the intricate behavior of the distribution, which prevents it to be satisfyingly modeled by a two-parameter model. For the bimodal behavior, the two-parameter Weibull function, which produces only a unimodal distribution, is simply inadequate to model it appropriately. Therefore, in recent years, alternative functions have been suggested for both unimodal and bimodal distributions, seeking more involved functions to better model these distributions. This article involves the modeling of observed wind speed probability density distributions using the main body of models found in the literature, namely, Rayleigh, Lognormal, two-parameter Weibull, three-parameter Weibull, and bimodal Weibull probability distribution functions. One of the important steps in the evaluation of different functions is the interpretation of the statistical parameters, namely, slope, $R2$⁠, mean bias error, and root mean squared error, as are presently used in this article. A novel statistical tool is developed in the present article using these four statistical parameters. The novel tool can be used to evaluate the relative performance of models when more than one model is involved or to determine the overall accuracy of a particular model for a specific site. The calculations are made based on the long term wind speed data collected at 4-s interval at the experimental site at Edinburgh Napier University.