An appraisal on some methods for estimating the 2-parameter weibull distribution with application to wind speeds sample

Six methods for estimating the Weibull shape and scale parameters are considered and compared in this paper. These methods are: the least squares method, weighted least squares method, method of moments, energy pattern factor method, method of L-moments and the maximum likelihood method. A simulation study as well as application to a real data set (wind speeds sample) was used to test the performance of different methods using the smallest mean square error criterion. Results from the simulation study indicated that the maximum likelihood method is the most efficient method when dealing with large sample sizes, while the weighted least squares method, method of moments and the method of L-moments were quite efficient for small and moderate sample sizes. The maximum likelihood method produced the best method when all six methods were applied to a wind speeds sample by possessing the smallest mean square error. A very useful result obtained from the study is that the weighted least squares method which performed considerably well in estimating the Weibull parameters. This is a rare incidence in many studies.