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Two R\'{e}nyi-type generalizations of the Shannon cross-entropy, theR\'{e}nyi cross-entropy and the Natural R\'{e}nyi cross-entropy, were recentlyused as loss functions for the improved design of deep learning generativeadversarial networks. In this work, we build upon our results in [1] byderiving the R\'{e}nyi and Natural R\'{e}nyi differential cross-entropymeasures in closed form for a wide class of common continuous distributionsbelonging to the exponential family and tabulating the results for ease ofreference. We also summarise the R\'{e}nyi-type cross-entropy rates betweenstationary Gaussian processes and between finite-alphabet time-invariant Markovsources.

R\'{e}nyi Cross-Entropy Measures for Common Distributions and Processes with Memory