Abstract
Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for . Its relationship to Kolmogorov–Sinai entropy and, for , to the recently introduced symbolic correlation integral are touched.
Highlights
Given a measurepreserving dynamical system (Ω, A, μ, T ), we look at the Rényi permutation entropy (RPE) for q = 2
We looked more closely at the recently introduced and used Rényi variant of permutation entropy, depending on a parameter q ∈ [0, ∞[, which is called
Giving a summary of first applications of RPE, and discussing RPE for some special parameter q, we mainly focused on the asymptotics of RPE for ordinal pattern length going to ∞
Summary
Since Bandt and Pompe [1] introduced the concept of permutation entropy (PE), it has been applied in different fields from biomedicine to econophysics (e.g., Zanin et al [2], and Amigò et al [3]) and developed into various directions. As. Rényi entropies depend on a parameter q ∈ [0, ∞[, there are different choices of RPE depending on q. The central aim of the paper is to discuss the asymptotics of RPE for increasing pattern length. This is motivated by the striking fact that, under certain assumptions, asymptotic. It first follows a short overview of first applications of the RPE. The concepts of RPE are introduced in empirical and model-based settings. With Corollary 1, the section contains the main new result of the paper relating RPE to Kolmogorov–Sinai entropy for q ∈ [0, 1] and measures with maximal entropy.
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