Different informational characteristics of cubic transmuted distributions

TL;DR

This paper explores the informational characteristics of cubic transmuted distributions by deriving entropy, Gini's mean difference, and Fisher information, and introduces new measures like cubic transmuted Shannon entropy and Gini's mean difference.

Contribution

It provides the first derivation of key information measures for CT distributions and introduces novel entropy and Gini's mean difference measures related to these distributions.

Findings

Derived Shannon entropy, Gini's mean difference, and Fisher information for CT distributions.

Established theoretical properties and connections with divergence measures.

Conducted simulation studies to evaluate the proposed information measures.

Abstract

Cubic transmuted (CT) distributions were introduced recently by \cite{granzotto2017cubic}. 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.