Mixture Fisher-Shannon information measure: Extensions and application

Abstract

The purpose of this paper is two-fold. In the first part, we introduce a novel information measure known as the mixture Fisher--Shannon information measure, motivated by de Bruijn's identity. We also propose and study a specific case of this measure called the difference information measure along with its Jensen version. Subsequently, the paper delves into an examination of their properties.  In the second part, we introduce $(p,\eta)$-Jensen difference Fisher--Shannon information measure. Additionally, we explore possible connections between this divergence measure and Jensen--Shannon entropy and Jensen--Fisher information measures. Our analysis not only examines theoretical foundations but also extends to practical applications. Specifically, we apply these measures to analyze time series data concerning the fish condition factor index, providing valuable insights into data interpretation.