基于广义刘维尔分数阶导数的熵公式

An Entropy Formulation Based on the Generalized Liouville Fractional Derivative.

作者信息

Ferreira Rui A C, Tenreiro Machado J

机构信息

Grupo Física-Matemática, Faculdade de Ciências, Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649-003 Lisboa, Portugal.

Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, R. Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal.

出版信息

Entropy (Basel). 2019 Jun 28;21(7):638. doi: 10.3390/e21070638.

DOI:10.3390/e21070638

PMID:33267352

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7515131/

Abstract

This paper presents a new formula for the entropy of a distribution, that is conceived having in mind the Liouville fractional derivative. For illustrating the new concept, the proposed definition is applied to the Dow Jones Industrial Average. Moreover, the Jensen-Shannon divergence is also generalized and its variation with the fractional order is tested for the time series.

摘要

本文提出了一种分布熵的新公式，该公式是在考虑刘维尔分数阶导数的情况下构想出来的。为了说明这一新概念，将所提出的定义应用于道琼斯工业平均指数。此外，还对詹森 - 香农散度进行了推广，并针对时间序列测试了其随分数阶的变化情况。