Abstract
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.
Highlights
Wind speed is a classic example of a stochastic variable
Weibull distribution is a continuous probability distribution named after Waloddi Weibull who described it in detail in 1951, it was first identified by Maurice Frechet in1927 and first applied by Rosin and Rammler in 1933 to describe the size distribution of particles
To estimate the Weibull parameters and using the least squares method (LSM), we first admit the linearization of the Weibull cumulative distribution function (CDF) given by (2) which has the form
Summary
Wind speed is a classic example of a stochastic variable. Due to this stochastic nature, its characteristics and behaviors in a given location can be captured by fitting specific probability distributions to a given wind speeds sample(s) collected over time. The 2-parameter Weibull distribution has become the most widely used probability distribution in wind speed analysis. Central to the use of the Weibull model in wind speed analysis is the estimation of the parameters of the Weibull distribution. Several methods for estimating the Weibull parameters have been proposed over the years. These methods can be classified into two broad categories, namely: graphical methods and statistical methods. Some commonly used graphical methods include the empirical cumulative distribution function plot methods , Weibull probability plot and hazard rate plot. The Weibull estimators obtained using statistical methods are generally more accurate but complex to deal with than their graphical counterpart.
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