Information flow between the systems can be quantified by using the measures that are derived from

entropies by observing the state variables. In this study, the mutual information and the transfer

entropy of the coupled Gaussian processes and the entropy of the bistable system have been

estimated for this purpose. Information measures of the systems have been obtained by the

histogram, kernel density estimator, k-nearest neighbor entropy estimator and kpN entropy

estimator for the different parameters. Normalized bias and normalized standard error have been

calculated to determine the performance of the estimation of the entropy measures. The optimal

parameters of the entropy estimators of information measures have been obtained. It is shown that

k-nearest neighbor entropy estimator has the best performance for the coupled Gaussian processes.

Additionally, the entropy of a nonlinear system i.e. the bistable system has been estimated. While

kernel density estimator and k-nearest neighbor entropy estimator have succeeded in achieving the

estimation of the entropy in the bistable system, it is shown that normalized bias and normalized

standard error of histogram and k-nearest neighbor method have high ratios. The entropy

estimations of the coupled dynamical systems have been estimated with considerable accuracy when

the optimal parameters of the entropy estimations have been used. The transfer entropy of a real

dataset has also been estimated via these methods. We have discussed the statistical significance of

the estimation methods of transfer entropy by using a hypothesis test. The study provides a way to

determine information measures that quantify the uncertainty of the systems and information flows

between the systems, accurately.