Advancing Shannon Entropy for Measuring Diversity in Systems
Joint Authors
Rajaram, R.
Castellani, B.
Wilson, A. N.
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-05-24
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science.
Part of the challenge is measuring it.
Shannon entropy H has been used to rethink diversity within probability distributions, based on the notion of information.
However, there are two major limitations to Shannon’s approach.
First, it cannot be used to compare diversity distributions that have different levels of scale.
Second, it cannot be used to compare parts of diversity distributions to the whole.
To address these limitations, we introduce a renormalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c.
Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of p^c(x) up to cumulative probability c.
We illustrate the utility of our approach by renormalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions for energy of subatomic particles.
The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions.
American Psychological Association (APA)
Rajaram, R.& Castellani, B.& Wilson, A. N.. 2017. Advancing Shannon Entropy for Measuring Diversity in Systems. Complexity،Vol. 2017, no. 2017, pp.1-10.
https://search.emarefa.net/detail/BIM-1143571
Modern Language Association (MLA)
Rajaram, R.…[et al.]. Advancing Shannon Entropy for Measuring Diversity in Systems. Complexity No. 2017 (2017), pp.1-10.
https://search.emarefa.net/detail/BIM-1143571
American Medical Association (AMA)
Rajaram, R.& Castellani, B.& Wilson, A. N.. Advancing Shannon Entropy for Measuring Diversity in Systems. Complexity. 2017. Vol. 2017, no. 2017, pp.1-10.
https://search.emarefa.net/detail/BIM-1143571
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143571