A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation

Table 7

L-skew (𝜏₃) and L-kurtosis (𝜏₄) results.

(a) 𝑛=25

Dist	Parameter	Estimate	95% bootstrap C.I.	Stand. error	Relative bias %
1	𝜏3=0.23	0.2043	0.2026,0.2061	0.00091	−11.2
	𝜏4=0.25	0.2343	0.2329,0.2357	0.00072	−6.3
2	𝜏3=−0.12	−0.1075	−0.1090,−0.1059	0.00086	−10.4
	𝜏4=0.20	0.1942	0.1931,0.1954	0.00058	−2.9
3	𝜏3=0	0.0015	−0.0004,0.0034	0.00098	—
	𝜏4=0.25	0.2413	0.2400,0.2425	0.00063	−3.5
4	𝜏3=0	0.00116	−0.00027,0.00249	0.00070	—
	𝜏4=0.1667	0.1654	0.1644,0.1664	0.00050	−0.76

(b) 𝑛=1000

Dist	Parameter	Estimate	95% bootstrap C.I.	Stand. error	Relative bias %
1	𝜏3=0.23	0.2291	0.2287,0.2294	0.00017	−0.39
	𝜏4=0.25	0.2494	0.2492,0.2497	0.00013	−0.24
2	𝜏3=−0.12	−0.1197	−0.1200,−0.1195	0.00013	—
	𝜏4=0.20	0.1999	0.1997,0.2001	0.00009	—
3	𝜏3=0	−0.0001	−0.0004,0.0003	0.00017	—
	𝜏4=0.25	0.2498	0.2496,0.2500	0.00010	—
4	𝜏3=0	−0.00004	−0.00026,0.00016	0.00011	—
	𝜏4=0.1667	0.1667	0.1665,0.1668	0.00007	—