Evaluating Transfer Entropy for Normal and γ-Order Normal Distributions

Since its introduction, transfer entropy has become a popular information-theoretic tool for detecting causal inference between two discretized random processes. By means of statistical tools we evaluate the transfer entropy of stationary processes whose continuous probability distributions are known. We study transfer entropy of processes coming from the family of γ-order generalized normal distribution. Applying Kullback-Leibler divergence we provide explicit expressions of the transfer entropy for processes which are normal, as well as for processes from the class of γ-order normal distributions. The results achieved in the paper for continuous time can be applied also to the discrete time case, concretely to the time series whose underlying process distribution is from the discussed classes.