Skew Student-t Distribution
Association Kendall’s Correlation
parameters coefficients coefficients
|
0.01 |
0.01 |
0.01 |
0.3293 |
0.3250 |
0.3299 |
0.3979 |
0.3887 |
0.4104 |
|
0.10 |
0.10 |
0.01 |
0.3933 |
0.3977 |
0.0451 |
0.4948 |
0.5028 |
0.0608 |
|
0.50 |
0.01 |
0.01 |
0.4805 |
0.0170 |
0.0164 |
0.6698 |
0.0412 |
0.0358 |
|
0.10 |
0.02 |
0.01 |
0.6430 |
0.1495 |
0.0760 |
0.7403 |
0.2261 |
0.1165 |
|
0.50 |
0.50 |
0.50 |
0.1473 |
0.1431 |
0.1471 |
0.2140 |
0.2009 |
0.1992 |
|
1.00 |
0.10 |
0.10 |
0.2785 |
0.0628 |
0.0617 |
0.4319 |
0.0939 |
0.0895 |
|
1.50 |
0.50 |
0.50 |
0.1455 |
0.0778 |
0.0761 |
0.2301 |
0.1127 |
0.1048 |
|
5.00 |
0.10 |
0.01 |
0.0893 |
0.0158 |
0.0054 |
0.1570 |
0.0298 |
0.0078 |
|
5.00 |
5.00 |
5.00 |
0.0235 |
0.0285 |
0.0252 |
0.0418 |
0.0447 |
0.0416 |
|
Skew Generalized Secant Hyperbolic Distribution | ||||||||
|
Association |
Kendall’s coefficients |
Correlation coefficients | ||||||
|
0.01 |
0.01 |
0.01 |
0.3231 |
0.3256 |
0.3248 |
0.3827 |
0.3824 |
0.3953 |
|
0.10 |
0.10 |
0.01 |
0.3965 |
0.3943 |
0.0447 |
0.4847 |
0.4737 |
0.0520 |
|
0.50 |
0.01 |
0.01 |
0.4806 |
0.0177 |
0.0159 |
0.6637 |
0.0422 |
0.0416 |
|
0.10 |
0.02 |
0.01 |
0.6416 |
0.1487 |
0.0755 |
0.7294 |
0.2234 |
0.1161 |
|
0.50 |
0.50 |
0.50 |
0.1429 |
0.1427 |
0.1443 |
0.2045 |
0.1944 |
0.1884 |
|
1.00 |
0.10 |
0.10 |
0.2791 |
0.0640 |
0.0611 |
0.4277 |
0.0921 |
0.0906 |
|
1.50 |
0.50 |
0.50 |
0.1431 |
0.0799 |
0.0786 |
0.2324 |
0.1142 |
0.1068 |
|
5.00 |
0.10 |
0.01 |
0.0925 |
0.0201 |
0.0048 |
0.1628 |
0.0354 |
0.0072 |
|
5.00 |
5.00 |
5.00 |
0.0219 |
0.0217 |
0.0209 |
0.0360 |
0.0356 |
0.0312 |
|
Skew Exponential Power Distribution | ||||||||
|
Association |
Kendall’s coefficients |
Correlation coefficients | ||||||
|
parameters | ||||||||
|
0.01 |
0.01 |
0.01 |
0.3231 |
0.3256 |
0.3248 |
0.3819 |
0.3820 |
0.3954 |
|
0.10 |
0.10 |
0.01 |
0.3965 |
0.3943 |
0.0447 |
0.4812 |
0.4709 |
0.0517 |
|
0.50 |
0.01 |
0.01 |
0.4806 |
0.0177 |
0.0159 |
0.6621 |
0.0421 |
0.0416 |
|
0.10 |
0.02 |
0.01 |
0.6416 |
0.1487 |
0.0755 |
0.7265 |
0.2229 |
0.1160 |
|
0.50 |
0.50 |
0.50 |
0.1429 |
0.1427 |
0.1443 |
0.2034 |
0.1935 |
0.1874 |
|
1.00 |
0.10 |
0.10 |
0.2791 |
0.0640 |
0.0611 |
0.4271 |
0.0917 |
0.0902 |
|
1.50 |
0.50 |
0.50 |
0.1431 |
0.0799 |
0.0786 |
0.2319 |
0.1137 |
0.1063 |
|
5.00 |
0.10 |
0.01 |
0.0925 |
0.0201 |
0.0048 |
0.1626 |
0.0354 |
0.0071 |
|
5.00 |
5.00 |
5.00 |
0.0219 |
0.0217 |
0.0209 |
0.0358 |
0.0355 |
0.0312 |
Table 1: Correlation and Kendall’s coefficients for tt∩ = «22 = ''l33 = 0 and marginals with
zero mean, unit variance, skewness equal to -0.5, 0, 0.5 and kurtosis equal to 5, 6, 8.