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Expectation Values and Variance Based on Lp-Norms
Southwest Research Institute, San Antonio, TX-78238, USA
Received: 4 August 2012; in revised form: 13 November 2012 / Accepted: 14 November 2012 / Published: 26 November 2012
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
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MDPI and ACS Style
Livadiotis, G. Expectation Values and Variance Based on Lp-Norms. Entropy 2012, 14, 2375-2396.
Livadiotis G. Expectation Values and Variance Based on Lp-Norms. Entropy. 2012; 14(12):2375-2396.
Livadiotis, George. 2012. "Expectation Values and Variance Based on Lp-Norms." Entropy 14, no. 12: 2375-2396.