Concepts and Recent Advances in Generalized Information Measures and Statistics

A.M. KOWALSKI; R. ROSSIGNOLI; E.M.F. CURADO

Bentham Science

Lugar: Sharja; Año: 2013 p. 414

978-1-60805-761-0

Since the introduction of the concept of information entropy by Claude Shannon in his famous 1948 article, quantifiers based on information theory have played an increasingly fundamental role in several fields. Different generalizations of the Shannon entropy have been developed, among them the R´enyi and Tsallis entropies, which have found important applications not only in physics but also in quite distinct areas such as biology, economy, cognitive sciences, etc. In addition, other information measures such as the Fisher information, which predates the Shannon entropy, and the more recent statistical complexities, have also proved to be useful and powerful tools in different scenarios, allowing in particular to analyze time series and data series independently of their sources. It is our goal to expose in this E-book, in a broadly accessible level, the basic concepts and some of the latest developments in the field of generalized information measures, understanding as such all those quantities which allow to obtain and quantify information from a probability distribution. Addressed not only to physicists, but also to researchers in other fields like biology, medicine, economics, etc, it offers through its chapters an overview of the main measures and techniques, together with some recent relevant applications which illustrate their potential. Its scope ranges from generalized entropies and the majorization based concept of disorder to complexity measures and metrics in probability space. It includes methods for extracting probability distributions from general data series and applications ranging from quantum entanglement to biology and brain modeling. A comprehensive list of references is also contained.