Dispersion indices based on Kerridge inaccuracy measure and Kullback-Leibler divergence

Abstract

Recently, a new dispersion index, as a measures of information, has been introduced and called varentropy. In this article, we introduce new measures of variability based on two measures of uncertainty, namely, the Kerridge inaccuracy measure and the Kullback-Leibler divergence. Their generating functions are considered and their infinite series representations are given. These new measures and associated properties, bounds and illustrative examples are all presented in detail. Finally, an application of Kullback-Leibler divergence and its dispersion index is illustrated by using the mean-variance rule.

KEYWORDS:

• Kerridge inaccuracy measure
• Kullback-Leibler divergence
• varentropy

AMS Subject Classification:

• 62N05
• 60E15
• 94A17

Acknowledgements

Francesco Buono, Camilla Calì and Maria Longobardi are members of the research group GNAMPA of INdAM (Istituto Nazionale di Alta Matematica). The authors also express their sincere thanks to the reviewers for their useful comments and suggestions which resulted in this much improved version.

Additional information

Funding

Francesco Buono and Maria Longobardi are partially supported by MIUR - PRIN 2017, project “Stochastic Models for Complex Systems”, no. 2017 JFFHSH. The present work was developed within the activities of the project 000009 ALTRI CDA 75 2021 FRA LINEA B funded by “Programma per il finanziamento della ricerca di Ateneo - Linea B” of the University of Naples Federico II.