Weighted Moments Estimators of the Parameters for the Extreme Value Distribution Based on the Multiply Type II Censored Sample

Table 1

MSEs of BLUE and WMEs of the scale parameter 𝜎 at 𝑁=15, 𝜎=1.0, and 𝜃=1.

Censoring scheme type II	𝑟	𝑘	𝑙	𝑠	The simulated MSEs of BLUE and exact MSEs of WMEs
					BLUE	WME1	WME2	WME3	WME4	WME/BLUE
Multiply	2	5	2	2	0.070396	0.067245	0.066049*	0.066182	0.067211	0.938249
	3	5	2	1	0.074345	0.069957	0.069488*	0.069732	0.069821	0.934669
	3	5	1	2	0.081776	0.077573	0.075709*	0.075784	0.077564	0.925810
	2	5	3	1	0.064955	0.061733	0.061551	0.061859	0.061543*	0.947471
	2	5	1	3	0.077774	0.074938	0.072323*	0.072350	0.074945	0.929912
	1	5	3	2	0.060664	0.058404	0.057795*	0.057900	0.058413	0.952707
	1	5	2	3	0.066040	0.064033	0.062353	0.062348*	0.064107	0.944094
	4	5	1	1	0.085554	0.079741	0.078920*	0.079045	0.079696	0.922458
	1	3	7	1	0.059028	0.056334	0.057378	0.057511	0.056253*	0.952984
	1	5	1	4	0.073128	0.071480	0.068433	0.068391*	0.071521	0.935223
Middle	0	3	6	0	0.045595	0.044507*	0.044635	0.044507*	0.044635	0.976138
					BLUE	WME5	WME6	WME7	WME8	WME/BLUE
Right	0	0	0	8	0.101814	0.132434	0.102793	0.132434	0.084350*	0.828472
Left	8	3	0	0	0.145212	0.127135*	0.127135*	0.349345	0.349345	0.875513
Doubly	7	3	0	2	0.169211	0.155749	0.145217*	0.477876	0.300771	0.858200

∗The smallest MSE among the proposed WMEs and BLUE.