Some Generalized Information and Divergence Generating Functions: Properties, Estimation, Validation and Application

Abstract

We propose Renyi information generating function and discuss its properties. The relation between the Renyi information generating function and Shannon entropy of order q > 0 is established and several bounds are obtained. Furthermore, we introduce Renyi divergence information generating function and discuss its effect under monotone transformations. We present non-parametric estimators of the Renyi information generating function and Golomb information generating function. For three coherent systems, we calculate the values of the Renyi information generating function and other well-established uncertainty measures and similar behaviour of the Renyi information generating function is observed. Finally, two chaotic maps are considered and then used to establish a validation of the proposed information generating function.