Extreme Value Distributions: An Overview of Estimation and Simulation

Table 8

Test of goodness of fit and root mean square error with .

Model	Log likelihood	AIC	BIC	A	W	RMSE
Gumbel-MLE	−3186828	6373660	6373683	0.5766605925	0.0723973654	0.0002133718
Gumbel-MOM	−3185937	6371879	6371902	16.477515229	2.6486539940	0.0002133731
Gumbel-MPS	−3185902	6371809	6371833	0.2699600000	0.0393380000	0.0002133710
Fréchet-MLE	−902633.6	1805271	1805295	388.21043208	74.546302650	0.0021526790
Fréchet-MOM	−906994.7	1813993	1814017	1342.0150000	148.35070000	0.0021630910
Fréchet-MPS	−902160.6	1804325	1804349	0.1119400000	0.5669100000	0.0021503496
Fréchet-3-MLE	−2733422	5466850	5466885	0.2180080150	0.0315607600	0.0001907248
Fréchet-3-MOM	−2807887	5615779	5615815	18333.010000	1797.1600000	0.0091505427
Fréchet-3-MPS	−2733422	5466850	5466885	0.2612600000	0.0366090000	0.0001906232
Weibull-MLE	−1520320	3040645	3040668	0.3530187557	0.0480795187	0.0020330810
Weibull-MOM	−1520320	3040645	3040668	0.4048516230	0.0580089449	0.0020330760
Weibull-MPS	−1520320	3040645	3040668	0.4294500000	0.0662080000	0.0020330750
Weibull-3-MLE	−1782463	3564932	3564967	0.3671212475	0.0553202892	0.0015759554
Weibull-3-MOM	Inf	Inf	Inf	Inf	18149.390000	1.1149331907
Weibull-3-MPS	−1782463	3564932	3564967	0.3011628000	0.0419733100	0.0015754390
GEVD-MLE	−3193448	6386901	6386937	0.2156288283	0.0336231660	0.0002303789
GEVD-MOM	−3291039	6582086	6582121	0.2515600000	0.0255580000	0.0002313981
GEVD-MPS	−3193448	6386901	6386937	0.1927100000	0.0260980000	0.0002303411