The Use of the Data Transformation Techniques in Estimating the Shape Parameter of the Weibull Distribution for the Wind Speed

Abstract

In recent years, the Weibull distribution has been commonly used and recommended to model the wind speed. Therefore, many estimators have been proposed to find the best method to estimate the parameters of the Weibull distribution. Particularly, the estimator based on regression procedures with the Weibull probability plot are often used because of its computational simplicity and graphical presentation. However, when the procedure is applied, in many cases heteroscedasticity or non-normality of the error terms may be encountered. One way to handle this problem is using transformation techniques. In this study, the regression estimation based on data transformation is considered to estimate the parameters of the Weibull distribution. The simulation results show that the considered estimator based on the data transformation for the shape parameter of the Weibull distribution provides better performance than least squares estimator in terms of bias and mean square errors for the most of the considered cases.

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

“…On the other hand, it should be noted that the error terms of the models given in Equations (11) and (12) are not identically distributed as mentioned by [9,[15][16][17]19,20], since x piq is beta distributed with parameters i and n´i`1 and, thus, the models (11) and (12) have a different variance for each i as earlier mentioned [9,19,20]. In other words, error terms of the previously mentioned models have no equal variance.…”

“…However, heteroscedasticity (non-constant variance) is present in the used regression model and, thus, LS estimates lose the efficiency property, even if most studies do not take into account this reality [9]. In such cases, the WLSE or alternative methods should be used [10][11][12][13][14][15][16][17][18][19][20]. It is well-known that when conducting the WLSE, the variances of the dependent variables are unknown and must be estimated to implement the WLSE procedure.…”