TABLE 4.
Distribution | Normal
|
Uniform
|
K1
|
K2
|
|
||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Average Skewness | Average Kurtosis | Average Skewness | Average Kurtosis | Average Skewness | Average Kurtosis | Average Skewness | Average Kurtosis | Average Skewness | Average Kurtosis | ||
Asymptotic Values | 01 | 01 | 01 | −0.6091 | −0.0102 | 10.9672 | −0.0302 | 31.0632 | 2.0121 | 6.0941 | |
| |||||||||||
Sample Size | |||||||||||
100 | 0.003 | −0.001 | 0.000 | −0.574 | −0.007 | 3.345 | 0.030 | 5.684 | 1.821 | 4.492 | |
200 | 0.000 | 0.001 | 0.000 | −0.595 | 0.022 | 4.517 | 0.027 | 7.755 | 1.913 | 5.185 | |
500 | 0.003 | 0.001 | 0.000 | −0.600 | −0.007 | 5.812 | −0.038 | 10.502 | 1.967 | 5.654 | |
1000 | −0.001 | 0.001 | 0.000 | −0.607 | −0.033 | 7.218 | −0.071 | 13.077 | 1.984 | 5.848 | |
5000 | 0.000 | 0.000 | 0.000 | −0.608 | 0.004 | 8.102 | 0.023 | 19.757 | 2.005 | 6.023 |
Note.
means theoretical values calculated based on Mattson (1997).
means simulation values calculated using one hundred randomly generated datasets of size 1,000,000.