On the Effects of Plotting Positions to the Probability Weighted Moments Method for the Generalized Logistic Distribution

초록

Five plotting positions are applied to the computation of probabilityweighted moments (PWM) on the parameters of the generalized logistic dis-tribution. Over a range of parameter values with some nite sample sizes,the eects of ve plotting positions are investigated via Monte Carlo simu-lation studies. Our simulation results indicate that the Landwehr plottingposition frequently tends to document smaller biases than others in the lo-cation and scale parameter estimations. On the other hand, the Weibullplotting position often tends to cause larger biases than others. The plot-ting position (i 0:35)=n seems to report smaller root mean square errors(RMSE) than other plotting positions in the negative shape parameter es-timation under small samples. In comparison to the maximum likelihood(ML) method under the small sample, the PWM do not seem to be betterthan the ML estimators in the location and scale parameter estimations doc-umenting larger RMSE. However, the PWM outperform the ML estimatorsin the shape parameter estimation when its magnitude is near zero. Sen-sitivity of right tail quantile estimation regarding ve plotting positions isalso examined, but superiority or inferiority of any plotting position is not observed.

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