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

Table 7

𝐿-skew (𝜏₃) and 𝐿-kurtosis (𝜏₄) results for the 𝐿-moment procedure.

Distribution	Parameter	Estimate	95% Bootstrap C.I.	St. error	RB%
		𝑛=25
1	𝜏3=0.3874	𝓉3=0.3637	0.3621, 0.3652	0.00078	−6.12
	𝜏4=0.2335	𝓉4=0.2149	0.2134, 0.2164	0.00078	−7.97
2	𝜏3=0.4641	𝓉3=0.4446	0.4431, 0.4461	0.00076	−4.20
	𝜏4=0.2265	𝓉4=0.2024	0.2007, 0.2042	0.00087	−10.64
3	𝜏3=0.1699	𝓉3=0.1614	0.1601, 0.1627	0.00066	−5.00
	𝜏4=0.1504	𝓉4=0.1472	0.1462, 0.1483	0.00054	−2.13
4	𝜏3=0.0	𝓉3=−0.0019	−0.0033,−0.0005	0.00071	—
	𝜏4=0.1667	𝓉4=0.1653	0.1643, 0.1663	0.00051	−0.84
		𝑛=1000
1	𝜏3=0.3874	𝓉3=0.3865	0.3863, 0.3868	0.00014	−0.23
	𝜏4=0.2335	𝓉4=0.2328	0.2325, 0.2331	0.00015	−0.30
2	𝜏3=0.4641	𝓉3=0.4633	0.4630, 0.4636	0.00015	−0.17
	𝜏4=0.2265	𝓉4=0.2255	0.2251, 0.2258	0.00019	−0.44
3	𝜏3=0.1699	𝓉3=0.1696	0.1694, 0.1698	0.00010	−0.18
	𝜏4=0.1504	𝓉4=0.1502	0.1501, 0.1504	0.00008	—
4	𝜏3=0.0	𝓉3=−0.0002	−0.0004,0.00002	0.00011	—
	𝜏4=0.1667	𝓉4=0.1667	0.1665, 0.1668	0.00007	—