Selection of regressand for fitting the extreme value distributions using the ordinary, weighted and generalized least-squares methods

Fitting the extreme value distributions to samples is needed in many reliability analysis problems. The ordinary, weighted and generalized least-squares methods (OL, WL and GL method) are used to fit extreme value distributions based on the moments of order statistics and adopted plotting positions. An analyst may consider the observed ordered sample or the reduced variate as the regressand. The choice of the regressand for the least-squares methods and their corresponding relative accuracy are not always clear. Simulation results are presented in this study to rank the performance of the OL, WL and GL methods in combination with the choice of the regressands to estimate the distribution parameters, quantiles and nonexceedance probability. Analysis results for the OL method are also presented by adopting different plotting positions. The results indicate that the use of the ordered sample as the regressand is preferred. In such a case, the GL method outperforms the OL and WL methods for small sample size; the performance of the OL, WL and GL methods are similar for the sample size greater than about 20. The application of the OL method can be of value, if the adopted plotting position approximates well the mean of order statistics.