Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure

• Published in: Physica A Vol. 518; pp. 177 - 189
• Main Author: Puertas-Centeno, D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.03.2019
• Subjects: Differential-escort distributions; LMC and LMC-Rényi complexity measures; Power-law-decaying probability densities; Shannon, Rényi and Tsallis entropies; Statistical complexity measures; Tsallis q-exponential densities; Power-law-decaying probability densities; Differential-escort distributions; Shannon, Rényi and Tsallis entropies; LMC and LMC-Rényi complexity measures; Statistical complexity measures; Tsallis q-exponential densities
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2018.11.066

Escort distributions have been shown to be very useful in a great variety of fields ranging from information theory, nonextensive statistical mechanics till coding theory, chaos and multifractals. In this work we give the notion and the properties of a novel type of escort density, the differential-escort densities, which have various advantages with respect to the standard ones. We highlight the behavior of the differential Shannon, Rényi and Tsallis entropies of these distributions. Then, we illustrate their utility to prove the monotonicity property of the LMC-Rényi complexity measure and to study the behavior of general distributions in the two extreme cases of minimal and very high LMC-Rényi complexity. Finally, this transformation allows us to obtain the Tsallis q-exponential densities as the differential-escort transformation of the exponential density. •Definition of the differential-escort transformation.•Basic and entropic properties of the differential-escort transformation.•Proof of the monotonicity property of the LMC-Rényi complexity measure.•Definition and characterization of the low and high complexity densities.•Application to power-law-decaying probability densities.