Characterizing Tukey ℎ and ℎℎ-Distributions through 𝐿-Moments and the 𝐿-Correlation

Table 11

Correlation (moderate) results for the 𝐿-moment procedure.

(a) 𝑛=25

Parameter	Estimate	95% Bootstrap C.I.	Standard error	Relative bias%
𝜂12=0.40	0.410	0.408, 0.412	0.0015	2.50
𝜂13=0.50	0.509	0.507, 0.511	0.0015	1.80
𝜂14=0.60	0.610	0.608, 0.611	0.0015	1.67
𝜂23=0.40	0.407	0.404, 0.409	0.0015	1.75
𝜂24=0.50	0.507	0.505, 0.509	0.0015	1.40
𝜂34=0.40	0.408	0.406, 0.410	0.0014	2.00

(b) 𝑛=1000

Parameter	Estimate	95% Bootstrap C.I.	Standard error	Relative bias%
𝜂12=0.40	0.4013	0.4010, 0.4017	0.00022	0.32
𝜂13=0.50	0.5017	0.5014, 0.5020	0.00022	0.34
𝜂14=0.60	0.6016	0.6014, 0.6019	0.00022	0.27
𝜂23=0.40	0.3999	0.3995, 0.4002	0.00022	—
𝜂24=0.50	0.5004	0.5001, 0.5007	0.00022	0.08
𝜂34=0.40	0.4003	0.3999, 0.4006	0.00021	—