Abstract
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.
Highlights
The Weibull distribution is a continuous probability distribution that was described by WaloddiWeibull in 1951 [1]
A model is proposed for the multivariate Weibull Probability Distribution Function (PDF), based on the classic parameters used in the definition of a univariate Weibull model and on the correlation coefficients among the marginal distributions
In most cases the parameters of the Weibull distributions defined in Equation (17) lie outside the intervals expressed in Equation (14), so, as it is explained in Section 2.1, RP does not represent the correlation matrix of the Pi variables
Summary
The Weibull distribution is a continuous probability distribution that was described by Waloddi. If the simultaneous behavior of a number of dependent variables, each of them described by a Weibull distribution, is being evaluated, a multivariate Weibull distribution needs to be used. A model is proposed for the multivariate Weibull PDF, based on the classic parameters used in the definition of a univariate Weibull model and on the correlation coefficients among the marginal distributions. It develops the change of variables from Normal to Weibull used in [12,13]. The structure of the paper is as follows: Section 2 derives the multivariate Weibull PDF from the Standard Normal one and outlines its application to wind speed and wind power, Section 3 deals with the bivariate Weibull PDF and Section 4 states the conclusions
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