Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis

Abstract

This paper introduce the belief Fisher–Shannon (BFS) information plane based on basic probability assignment concept. Moreover, upper and lower bounds of BFS information are also presented. In addition, BFS information plane is extended to belief Fisher–Rényi and fractional belief Fisher–Shannon ones, whose are based on Generalized Rényi and fractional Deng entropies, respectively. This study is exemplified by a simulation study of Logistic, Chebyshev, and Hénon chaotic map time series; and two applications related to fish condition factor and ozone pollutant time series. Time series were discretized using Freedman–Diaconis rule as a histogram estimator. Results indicate that proposed information planes based on histogram estimator provides a more efficient method with respect to parametric and non-parametric methods, such as one based on kernel density function. Therefore, our findings suggest that proposed information planes could be an appropriate tool to better investigate the complex dynamics of these signals.