極値分布の母数推定法の比較評価

Abstract

This paper compares parameter estimation methods for the Gumbel distributionand the generalized extreme-value (GEV) distribution by using the Monte Carlosimulation technique with changing sample size N=10, 20, …, 1000.The methods considered for the Gumbel distribution are the methods ofmoments (MoM), maximum likelihood estimation (MLE), probability weightedmoments (PWM), least-squares (LS) with the Weibull or the Hazen plottingformula, and maximum entropy principle (PME). In terms of the root mean squareerror (RMSE) of the quantile estimates, the MLE is the best among these. ThePWM gives the least biased estimation, followed by the MoM, PME and MLE. Thedifference of these is small. For the GEV distribution, the MoM, MLE and PWM arecompared. In terms of both the RMSE and bias the PWM is the best.