An L-Moment-Based Analog for the Schmeiser-Deutsch Class of Distributions

Table 8

𝐿-skew (𝜏₃) and 𝐿-kurtosis (𝜏₄) results for distributions 2 and 4 in Table 1.

Dist	Parameter	Estimate	95% bootstrap C.I.	Standard error	Relative bias %
𝑛=25
2	𝜏3=0.0	0.0002	−0.0014, 0.0018	0.00079	—
	𝜏4=0.2857	0.2981	0.2968, 0.2993	0.00063	4.34
4	𝜏3=−0.8414	−0.8638	−0.8647, −0.8628	0.00049	2.66
	𝜏4=0.6483	0.6956	0.6935, 0.6975	0.00102	7.30
𝑛=1000
2	𝜏3=0.0	−0.0001	−0.0003, 0.0001	0.00010	—
	𝜏4=0.2857	0.2860	0.2859, 0.2862	0.00008	0.11
4	𝜏3=−0.8414	−0.8422	−0.8423, −0.8420	0.00007	0.095
	𝜏4=0.6483	0.6498	0.6495, 0.6501	0.00015	0.23