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

Table 10

Correlation (moderate) results for the conventional moment procedure.

(a) 𝑛=25

Parameter	Estimate	95% Bootstrap C.I.	Standard error	Relative bias%
𝜌^∗12=0.40	0.424	0.422, 0.427	0.0014	6.00
𝜌^∗13=0.50	0.522	0.520, 0.524	0.0014	4.40
𝜌^∗14=0.60	0.624	0.622, 0.626	0.0013	4.00
𝜌^∗23=0.40	0.416	0.414, 0.418	0.0013	4.00
𝜌^∗24=0.50	0.516	0.514, 0.518	0.0013	3.20
𝜌^∗34=0.40	0.410	0.408, 0.412	0.0013	2.50

(b) 𝑛=1000

Parameter	Estimate	95% Bootstrap C.I.	Standard Error	Relative Bias%
𝜌^∗12=0.40	0.4020	0.4016, 0.4023	0.00024	0.50
𝜌^∗13=0.50	0.5022	0.5018, 0.5025	0.00024	0.44
𝜌^∗14=0.60	0.6023	0.6020, 0.6026	0.00024	0.38
𝜌^∗23=0.40	0.4005	0.4001, 0.4008	0.00021	0.12
𝜌^∗24=0.50	0.5010	0.5007, 0.5013	0.00021	0.20
𝜌^∗34=0.40	0.4003	0.4000, 0.4006	0.00020	0.08