Extreme Value Distributions: An Overview of Estimation and Simulation

Table 6

Maximum product of spacings (MPS).

Parameter	Gumbel dist	2-Fréchet dist	3-Fréchet dist	2-Weibull dist	3-Weibull dist	GEV-distribution
N = 1,000	= 5,  = 9	= 2,  = 5	= 1,  = 5,  = 3,	= 3,  = 7	= 3,  = 1,  = 5,	= 1,  = 3,  = 0.01
Location	5.107336	—	1.181352	—	3.0144140	1.136788370
95% CI	(4.03858, 6.176092)	—	(−0.023294, 2.385998)	—	(2.439769, 3.589059)	(0.882695, 1.39088)
CP	0.979	—	0.965	—	0.961	0.959
Bias	0.1073360	—	0.1813520	—	0.0144140	0.13678837
MSE	0.0118304	—	0.0332816	—	0.0002972	0.01872854
Scale	8.923836	1.990858	4.737531	2.999377	0.9868423	3.085039300
95% CI	(8.006222, 9.84145)	(1.905312, 2.076404)	(3.488991, 5.986071)	(2.781011, 3.217743)	(0.679259, 1.294426)	(2.845176, 3.324902)
CP	0.981	0.978	0.968	0.984	0.974	0.979
Bias	−0.0761640	−0.00914200	−0.26246900	−0.00062300	−0.01315770	0.08503930
MSE	0.00602903	8.55584E − 5	0.069312226	1.33043E − 05	0.000198752	0.00724726
Shape	—	5.015951	2.918228	7.162783	4.9621254	0.009968900
95% CI	—	(4.93862, 5.093282)	(1.991924, 3.844532)	(6.938631, 7.386935)	(4.539782, 5.384468)	(−0.003507, 0.023445)
CP	—	0.959	0.964	0.958	0.972	0.967
Bias	—	0.01595100	−0.08177200	0.16278300	−0.037874600	−3.110E − 05
MSE	—	0.00025605	0.00691907	0.02651191	0.001482802	5.0159E − 08
N  = 1,000,000	= 3,  = 5	= 15,  = 30	= 0,  = 30,  = 10,	= 10,  = 10	= 0.5,  = 13,  = 10,	= 3,  = 5,  = 0.01
Location	2.998510	—	0.01248723	—	0.4794425	3.003037123
95% CI	(2.640391, 3.356629)	—	(−0.506537, 0.531512)	—	(−0.281934, 1.240819)	(2.863204, 3.14287)
CP	0.984	—	0.978	—	0.968	0.988
Bias	−0.00149000	—	0.012487230	—	−0.020557500	0.003037123
MSE	2.25348E − 06	—	0.000156001	—	0.000422762	9.22921E − 06
Scale	4.997087	14.99970	29.99258016	9.999803	13.018940	5.004417502
95% CI	(4.611407, 5.382767)	(14.85415, 15.14525)	(29.25693, 30.72823)	(9.650049, 10.34956)	(12.46146, 13.57642)	(4.828128, 5.180707)
CP	0.989	0.997	0.991	0.998	0.987	0.986
Bias	−0.00291300	−0.00030000	−0.00741984	−0.00019700	0.018940000	0.004417502
MSE	8.52429E − 06	9.55146E − 08	5.51949E − 05	7.06525E − 08	0.000358804	1.95224E − 05
Shape	—	30.02264	9.99751933	9.992998	10.010710	0.009833649
95% CI	—	(29.84531, 30.19997)	(9.271215, 10.72382)	(9.550806, 10.43519)	(9.568518, 10.4529)	(−0.057776, 0.077444)
CP	—	0.953	0.994	0.992	0.943	0.998
Bias	—	0.02264000	−0.00248067	−0.00700200	0.0107100	−0.000166351
MSE	—	0.00051257	6.29104E − 06	4.90789E − 05	0.0001147	2.88626E − 08