Multivariate Weibull Distribution for Wind Speed and Wind Power Behavior Assessment

The goal of this paper is to show how to derive the multivariate Weibull probability density function from the multivariate Standard Normal one and to show its applications. Having Weibull distribution parameters and a correlation matrix as input data, the proposal is to obtain a precise multivariate Weibull distribution that can be applied in the analysis and simulation of wind speeds and wind powers at different locations. The main advantage of the distribution obtained, over those generally used, is that it is defined by the classical parameters of the univariate Weibull distributions and the correlation coefficients and all of them can be easily estimated. As a special case, attention has been paid to the bivariate Weibull distribution, where the hypothesis test of the correlation coefficient is defined.