A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and 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	0.4075	0.4048, 0.4100	0.00157	1.88
𝜂13=0.50	0.5060	0.5036, 0.5081	0.00156	1.20
𝜂14=0.60	0.6065	0.6044, 0.6083	0.00156	1.08
𝜂23=0.40	0.4071	0.4048, 0.4096	0.00147	1.78
𝜂24=0.50	0.5083	0.5060, 0.5103	0.00148	1.66
𝜂34=0.40	0.4068	0.4042, 0.4091	0.00149	1.70

(b) 𝑛=1000

Parameter	Estimate	95% bootstrap C.I.	Standard error	Relative bias%
𝜂12=0.40	0.4000	0.3996, 0.4004	0.00024	—
𝜂13=0.50	0.5001	0.4997, 0.5005	0.00024	—
𝜂14=0.60	0.6002	0.5999, 0.6004	0.00024	—
𝜂23=0.40	0.3996	0.3993, 0.4000	0.00022	—
𝜂24=0.50	0.5001	0.4998, 0.5004	0.00022	—
𝜂34=0.40	0.4000	0.3996, 0.4003	0.00022	—