A Method for Simulating Burr Type III and Type XII Distributions through 𝐿-Moments and 𝐿-Correlations

Table 6

Skew (𝛾₃) and kurtosis (𝛾₄) results for the conventional moment procedure.

Distribution	Parameter	Estimate	95% Bootstrap C.I.	St. error	RB%
		𝑛=25
1	𝛾3=4.2212	𝑔3=1.75	1.7397, 1.7597	0.00510	−58.54
	𝛾4=59.4545	𝑔4=3.34	3.2911, 3.3871	0.02430	−94.38
2	𝛾3=2.8284	𝑔3=2.151	2.1428, 2.1596	0.00429	−23.95
	𝛾4=12.0	𝑔4=4.215	4.1715, 4.2614	0.02306	−64.88
3	𝛾3=1.1395	𝑔3=0.7929	0.7859, 0.7994	0.00346	−30.42
	𝛾4=2.4	𝑔4=0.5014	0.4786, 0.5220	0.01111	−79.11
4	𝛾3=0.0	𝑔3=−0.051	−0.0585, −0.0430	0.00391	—
	𝛾4=1.2	𝑔4=0.3396	0.3243, 0.3552	0.00791	−71.70
		𝑛=1000
1	𝛾3=4.2212	𝑔3=3.606	3.5888, 3.6275	0.00972	−14.57
	𝛾4=59.4545	𝑔4=26.29	25.8657, 26.7366	0.22370	−55.78
2	𝛾3=2.8284	𝑔3=2.761	2.7548, 2.7681	0.00335	−2.38
	𝛾4=12.0	𝑔4=10.17	10.0615, 10.3107	0.06265	−15.25
3	𝛾3=1.1395	𝑔3=1.124	1.1219, 1.1266	0.00122	−1.36
	𝛾4=2.4	𝑔4=2.266	2.2451, 2.2861	0.01048	−5.58
4	𝛾3=0.0	𝑔3=−0.0045	−0.0064, −0.0025	0.00101	—
	𝛾4=1.2	𝑔4=1.158	1.1487, 1.1683	0.00498	−3.5