A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and 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	0.4517	0.4498, 0.4536	0.00123	12.93
𝜌^∗13=0.50	0.5492	0.5473, 0.5512	0.00143	9.84
𝜌^∗14=0.60	0.6505	0.6490, 0.6520	0.00134	8.42
𝜌^∗23=0.40	0.4226	0.4203, 0.4247	0.00137	5.65
𝜌^∗24=0.50	0.5170	0.5150, 0.5189	0.00135	3.40
𝜌^∗34=0.40	0.4155	0.4133, 0.4178	0.00136	3.88

(b) 𝑛=1000

Parameter	Estimate	95% bootstrap C.I.	Standard error	Relative bias%
𝜌^∗12=0.40	0.4076	0.4072, 0.4079	0.00023	1.90
𝜌^∗13=0.50	0.5061	0.5057, 0.5066	0.00030	1.22
𝜌^∗14=0.60	0.6071	0.6067, 0.6075	0.00031	1.18
𝜌^∗23=0.40	0.4026	0.4023, 0.4030	0.00022	0.65
𝜌^∗24=0.50	0.5014	0.5011, 0.5017	0.00021	0.28
𝜌^∗34=0.40	0.4007	0.4004, 0.4011	0.00021	0.18