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

D. Puertas-Centeno

Physica A: Statistical Mechanics and its Applications, 2019, vol. 518, issue C, 177-189

Abstract: 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.

Keywords: Differential-escort distributions; Shannon, Rényi and Tsallis entropies; Statistical complexity measures; LMC and LMC-Rényi complexity measures; Tsallis q-exponential densities; Power-law-decaying probability densities (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:518:y:2019:i:c:p:177-189

DOI: 10.1016/j.physa.2018.11.066

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