Distribution p Σ12 ν1 ν2 Uniform(0, 1) 0.3 -0.3 0 -1.20 0.3000 -0.3013 0.0001 -1.1930   0.3 0.4 0 -1.20 0.3000 0.4009 0.0001 -1.1971   0.5 -0.3 0 -1.20 0.5000 -0.3017 0.0000 -1.1923   0.5 0.4 0 -1.20 0.5000 0.4019 -0.0002 -1.1969 Laplace(1,1) 0.3 -0.3 0 3.0 0.3000 -0.2986 -0.0003 2.9982   0.3 0.4 0 3.0 0.3000 0.3943 0.0007 2.9991   0.5 -0.3 0 3.0 0.5000 -0.2969 -0.0006 3.0130   0.5 0.4 0 3.0 0.5000 0.3988 0.0011 2.9976 Normal mixture 0.3 -0.3 0 -0.9582 0.3000 -0.3015 -0.0002 -0.9581 (1,3,1,1,0.5) 0.3 0.4 0 -0.9582 0.3000 0.4021 -0.0003 -0.9582   0.5 -0.3 0 -0.9582 0.5000 -0.3033 0.0001 -0.9580   0.5 0.4 0 -0.9582 0.5001 0.4008 0.0000 -0.9579 Beta(4,2) 0.3 -0.3 -0.4677 -0.375 0.3000 -0.3009 -0.4673 -0.3756   0.3 0.4 -0.4677 -0.375 0.3000 0.3979 -0.4676 -0.3758   0.5 -0.3 -0.4677 -0.375 0.5000 -0.3019 -0.4681 -0.3751   0.5 0.4 -0.4677 -0.375 0.5000 0.4013 -0.4678 -0.3754 χ2(32) 0.3 -0.3 0.5 0.375 0.3000 -0.2987 0.4996 0.3752   0.3 0.4 0.5 0.375 0.3000 0.4013 0.4998 0.3751   0.5 -0.3 0.5 0.375 0.5000 -0.3000 0.4992 0.3755   0.5 0.4 0.5 0.375 0.5000 0.3999 0.4994 0.3744

Table 1: Specified parameter values for proportion, correlation, skewness and kurtosis, and empirical estimates averaged across N=1000 simulation replicates for five continuous distributions in a bivariate setting with n=10000 data points.