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Entropy 2012, 14(12), 2375-2396; doi:10.3390/e14122375
Article

Expectation Values and Variance Based on Lp-Norms

Received: 4 August 2012 / Revised: 13 November 2012 / Accepted: 14 November 2012 / Published: 26 November 2012
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Abstract

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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

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