Comparison of four mutual information estimators applied on the simple lognormal bivariate distribution presented in Sect. 2.1. The dashed black line corresponds to the theoretical value. The 1σ interval is not shown for the simple canonical correlation-based estimator as it appears to be asymptotically biased. The Kraskov estimator (in blue) converges to the correct value for a large number of simulated observations N. The CC estimator is used with three preprocessing: no preprocessing, log and Gaussian reparametrization. As the joint distribution is non-Gaussian, the no-preprocessing case does not converge to the theoretical value. However, the other two preprocessing transform it to a Gaussian, the associated CC estimators converge to the theoretical value for large values of N.