Joint distribution for V1 and V2 V2 V1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.006 0.017 0.028 0.037 0.044 0.048 0.049 0.050 0.050 0.2 0.013 0.043 0.081 0.120 0.156 0.181 0.193 0.198 0.200 0.3 0.017 0.061 0.124 0.197 0.273 0.331 0.364 0.381 0.387 0.4 0.019 0.071 0.149 0.248 0.358 0.449 0.505 0.535 0.548 0.5 0.019 0.076 0.164 0.281 0.417 0.537 0.616 0.663 0.683 0.6 0.020 0.078 0.173 0.301 0.456 0.600 0.701 0.763 0.793 0.7 0.020 0.079 0.177 0.312 0.481 0.642 0.760 0.837 0.877 0.8 0.020 0.080 0.179 0.318 0.494 0.667 0.798 0.887 0.936 0.9 0.020 0.080 0.180 0.320 0.499 0.678 0.816 0.913 0.970 What is the Copula correlation? What is the main application? 56 Map V2 with a normal distribution V2 value Percentile of U2 value Distribution 0.1 2.00 -2.05 0.2 8.00 -1.41 0.3 18.00 -0.92 0.4 32.00 -0.47 0.5 50.00 0.00 0.6 68.00 0.47 0.7 82.00 0.92 0.8 92.00 1.41 0.9 98.00 2.05 55 Map V1 with Normal Distributions V1 value Percentile of U1 value Distribution 0.1 5.00 -1.64 0.2 20.00 -0.84 0.3 38.75 -0.29 0.4 55.00 0.13 0.5 68.75 0.49 0.6 80.00 0.84 0.7 88.75 1.21 0.8 95.00 1.64 0.9 98.75 2.24 54 54