biases, root mean square errors (RMSEs) and standard deviations (SDs), along with average theoretical variances, scaled by 100, for the MLEs of the main parameters of interest under different copula choices and margins. The theoretical variances of the MLEs are obtained via the gradients and the Hessian that were computed numerically during the maximization process. The results for the variability parameters are presented in Table 3 and Table 4 of the Supplementary material.

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                    margin   copula                          $\pi_{11}$   $\pi_{12}$   $\pi_{01}$   $\pi_{02}$      $\pi_{11}$   $\pi_{12}$   $\pi_{01}$   $\pi_{02}$
  Bias              normal   BVN                               -0.07        -0.29        -0.21        -0.05            1.95         1.74         5.08         0.78
                             Cln{$0^\circ,270^\circ$}          -0.10        -0.29        -0.32        -0.06            2.00         1.79         4.99         0.78
                             Cln{$180^\circ,90^\circ$}         -0.68        -0.87        -0.10        -0.03            1.43         1.23         5.17         0.80
                             Frank                             -1.33        -1.47         0.06         0.03            0.53         0.34         5.29         0.84
                    beta     BVN                               -1.58        -1.71        -4.31        -1.22            0.11        -0.05         0.03        -0.02
                             Cln{$0^\circ,270^\circ$}          -1.64        -1.75        -4.46        -1.24            0.13        -0.03        -0.06        -0.02
                             Cln{$180^\circ,90^\circ$}         -2.40        -2.49        -4.26        -1.23           -0.68        -0.83         0.08        -0.01
                             Frank                             -2.64        -2.73        -4.14        -1.15           -1.18        -1.33         0.25         0.07
  SD                normal   BVN                                3.61         3.48         3.39         0.84            3.69         3.64         3.18         0.69
                             Cln{$0^\circ,270^\circ$}           3.62         3.50         3.42         0.84            3.70         3.65         3.23         0.69
                             Cln{$180^\circ,90^\circ$}          3.89         3.76         3.49         0.86            3.96         3.91         3.27         0.71
                             