Different informational characteristics of cubic transmuted distributions

Cubic transmuted (CT) distributions were introduced recently by Granzotto, Louzada and Balakrishnan (Journal of Statistical Computation and Simulation87 (2017) 2760–2778). In this article, we derive Shannon entropy, Gini’s mean difference and Fisher information (matrix) for CT distributions and establish some of their theoretical properties. In addition, we propose cubic transmuted Shannon entropy and cubic transmuted Gini’s mean difference. The CT Shannon entropy is expressed in terms of Kullback-Leibler divergences, while the CT Gini’s mean difference is shown to be connected with energy distances. We show that the Kullback-Leibler and Chi-square divergences are free of the underlying parent distribution. Finally, we carry out some simulation studies for the proposed information measures from an inferential viewpoint.