Next Article in Journal
Entropy-Based Block Processing for Satellite Image Registration
Previous Article in Journal
Periodic Cosmological Evolutions of Equation of State for Dark Energy 
Entropy 2012, 14(12), 2375-2396; doi:10.3390/e14122375

Expectation Values and Variance Based on Lp-Norms

Southwest Research Institute, San Antonio, TX-78238, USA
Received: 4 August 2012 / Revised: 13 November 2012 / Accepted: 14 November 2012 / Published: 26 November 2012
View Full-Text   |   Download PDF [480 KB, 24 February 2015; original version 24 February 2015]   |  


This analysis introduces a generalization of the basic statistical concepts of expectation values and variance for non-Euclidean metrics induced by Lp-norms. The non-Euclidean Lp means are defined by exploiting the fundamental property of minimizing the Lp deviations that compose the Lp variance. These Lp expectation values embody a generic formal scheme of means characterization. Having the p-norm as a free parameter, both the Lp-normed expectation values and their variance are flexible to analyze new phenomena that cannot be described under the notions of classical statistics based on Euclidean norms. The new statistical approach provides insights into regression theory and Statistical Physics. Several illuminating examples are examined.
Keywords: expectation values; variance; optimization; fitting methods; Lp-norms; timeseries analysis expectation values; variance; optimization; fitting methods; Lp-norms; timeseries analysis
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

Livadiotis, G. Expectation Values and Variance Based on Lp-Norms. Entropy 2012, 14, 2375-2396.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert