Different Methods for Estimating Location Parameter & Scale Parameter for Extreme Value Distribution

Abstract

      In this study, different methods were used for estimating location parameter  and scale parameter for extreme value distribution, such as maximum likelihood estimation (MLE) , method of moment  estimation (ME),and approximation  estimators based on percentiles which is called white method in estimation, as the extreme value distribution is one of exponential distributions. Least squares estimation (OLS) was used, weighted least squares estimation (WLS), ridge regression estimation (Rig), and adjusted ridge regression estimation (ARig) were used. Two parameters for expected value to the percentile  as estimation for distribution functionwere used .Several models from extreme value distribution were used for data generating , for different sample sizes (small, medium, and large).The results were obtained  by  using  simulation  technique, Programs written using MATLAB program were used. To compare the performance for the methods used in this study, the mean squared error criterion (MSE) and mean absolute squared error criterion (MAPE) for two parameters for the extreme value distribution were used as criterion to compare the performance for the methods . The results showing according to the two criterions (MSE &MAPE), that maximum likelihood estimation is the best of all of the others methods, following by the method of moment estimation . The adjusted ridge regression estimation method have best performance for the suggested parameter for expected value to the percentile which was used as estimation for distribution function.