Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure
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-...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/40222 |
| Acceso en línea: | https://hdl.handle.net/10115/40222 |
| Access Level: | acceso embargado |
| Palabra clave: | 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 |
| Sumario: | 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. |
|---|