On The Estimation of Parameters in a Weibull Wind Model and its Application to Wind Speed Data from Maiduguri, Borno State, Nigeria

Abstract

Four methods of parameter estimation of the Weibull distribution are examined. These are maximum likelihood, method of moments, optimization and regression methods. It is shown how the parameters of the distribution can be obtained by each of these four methods using iterative techniques in numerical methods. These are illustrated by fitting Weibull and Rayleigh models to the wind speed data from Maiduguri. The model fits obtained by using each of these four methods of estimation are tested using four goodness–of –fit tests and compared using Root-Mean-Square-Error estimates. Results show that (i) only the Weibull model fits the data, (ii) differences in the corresponding estimates of parameters so obtained are thin, (iii) differences in the root-mean-square-error (RMSE) estimates are thin (iv) the RMSE estimates for the regression method is consistently the smallest; that is, the best fit and (v) the regression method is also the easiest to implement in obtaining estimates of the Weibull parameters and their standard errors. These indicate that the regression method could be a user’s first choice in obtaining parameter estimates for a Weibull wind model.

Keywords: Parameter Estimation, Goodness-of-Fit tests, Root-Mean-Square-Error, Weibull distribution, Wind speed data, Wegstein’s iterative method, optimization method, R programming language, Renewable Energy, New-Raphson iterative solution.