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

Table 7

Skew (𝛼₃) and kurtosis (𝛼₄) results for distributions 2 and 4 in Table 1.

Dist	Parameter	Estimate	95% bootstrap C.I.	Standard error	Relative bias %
𝑛=25
2	𝛼3=0.0	0.0019	−0.0055, 0.0094	0.00381	—
	𝛼4=0.7692	1.166	1.1496, 1.1821	0.00825	51.59
4	𝛼3=−4.181	−3.581	−3.5917, −3.5702	0.00549	−14.35
	𝛼4=18.21	13.61	13.5278, 13.6973	0.04337	−25.26
𝑛=1000
2	𝛼3=0.0	−0.0005	−0.0013, 0.0004	0.00042	—
	𝛼4=0.7692	0.7798	0.7778, 0.7817	0.00100	1.38
4	𝛼3=−4.181	−4.190	−4.1936, −4.1866	0.00177	0.22
	𝛼4=18.21	18.44	18.4046, 18.4738	0.01775	1.26