Most studies involving simultaneous electroencephalographic (EEG) and functional magnetic resonance imaging (fMRI) data rely on the first-order, affine-linear correlation of EEG and fMRI features within the framework of the general linear model. An alternative is the use of information-based measures such as mutual information and entropy, which can also detect higher-order correlations present in the data. The estimate of information-theoretic quantities might be influenced by several parameters, such as the numerosity of the sample, the amount of correlation between variables, and the discretization (or binning) strategy of choice. While these issues have been investigated for invasive neurophysiological data and a number of bias-correction estimates have been developed, there has been no attempt to systematically examine the accuracy of information estimates for the multivariate distributions arising in the context of EEG-fMRI recordings. This is especially important given the differences between electrophysiological and EEG-fMRI recordings. In this study, we drew random samples from simulated bivariate and trivariate distributions, mimicking the statistical properties of EEG-fMRI data. We compared the estimated information shared by simulated random variables with its numerical value and found that the interaction between the binning strategy and the estimation method influences the accuracy of the estimate. Conditional on the simulation assumptions, we found that the equipopulated binning strategy yields the best and most consistent results across distributions and bias correction methods. We also found that within bias correction techniques, the asymptotically debiased (TPMC), the jackknife debiased (JD), and the best upper bound (BUB) approach give similar results, and those are consistent across distributions.