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

Table 6

Skew (𝛼₃) and Kurtosis (𝛼₄) results for the conventional moment procedure.

(a) n = 25

Dist	Parameter	Estimate	95% Bootstrap C.I.	Standard error	Relative bias %
1	𝛼3=4.502	1.259	1.246,1.272	0.0065	−72.0
	𝛼4=129.5	3.286	3.230,3.340	0.0280	−97.5
2	𝛼3=−1.356	−0.6655	−0.6756,−0.6551	0.0053	−50.9
	𝛼4=7.518	1.657	1.625,1.694	0.0175	−78.0
3	𝛼3=0	0.0093	−0.0052,0.0228	0.0071	—
	𝛼4=9.674	2.374	2.335,2.411	0.0194	−75.5
4	𝛼3=0	0.0068	−0.0016,0.0150	0.0042	—
	𝛼4=1.2	0.7011	0.6826,0.7202	0.0096	−41.6

(b) n = 1000

Dist	Parameter	Estimate	95% bootstrap C.I.	Standard error	Relative bias %
1	𝛼3=4.502	3.285	3.260,3.311	0.0128	−27.0
	𝛼4=129.5	29.16	28.56,29.75	0.3057	−77.5
2	𝛼3=−1.356	−1.286	−1.293,−1.279	0.0037	−5.2
	𝛼4=7.518	6.260	6.157,6.373	0.0555	−16.7
3	𝛼3=0	−0.0011	−0.0110,0.0090	0.0051	—
	𝛼4=9.674	8.016	7.897,8.152	0.0644	−17.1
4	𝛼3=0	−0.0003	−0.0019,0.0019	0.0010	—
	𝛼4=1.2	1.179	1.173,1.185	0.0033	−1.79