The overlapping or similarity coefficient is defined to be a measure of the similarity between two probability distributions. This coefficient is applied in various fields, such as signal processing, econometrics, ecology and particularly in meteorology. The objective of this study is to construct an index of similarity of wind speed distributions based on the overlapping coefficients and to apply this index to wind speed data in the Sultanate of Oman. We will use both parametric and nonparametric approaches to estimate the overlapping parameters of two distributions. First, in the parametric approach, we will fit parametric distributions, such as Burr type II, to the wind speed data and then we will estimate the overlapping coefficients. Whereas, in the nonparametric approach, we will estimate the overlapping coefficient by the Kernel Density Estimator (KDE) using the plug-in method. The main results are obtained in this thesis as follow. Although, the Burr distribution fits most of wind speed in stations, but it is iii difficult be adequate for all the station's data. So, KDE can be an alternative method to fit the data. Furthermore, the most of the coefficients and are close to each other. Also, it is noticed in all the cases the measures have this relationship of As well as , it has shown that the coefficients of KDE and Burr distributions and 95% Bootstraps Intervals are agreements. For the degree of similarity between pair stations, the distribution of wind speed between Masirah and Rustaq stations is a high different, because there are difference in geography area between these two sites. The most of the pair stations are moderate similar.