Renyi entropy measures of heart rate Gaussianity

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q=1) and quadratic entropy (q=2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.