On the Convergence and Law of Large Numbers for the Non-Euclidean Lp -Means

Livadiotis, George

doi:10.3390/e19050217

Open AccessArticle

On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means

by

George Livadiotis

Space Science and Engineering, Southwest Research Institute, San Antonio, TX 78238, USA

Entropy 2017, 19(5), 217; https://doi.org/10.3390/e19050217

Submission received: 18 January 2017 / Revised: 13 April 2017 / Accepted: 9 May 2017 / Published: 11 May 2017

Download

Browse Figures

Versions Notes

Abstract

This paper describes and proves two important theorems that compose the Law of Large Numbers for the non-Euclidean

L^{p}

-means, known to be true for the Euclidean

L^{2}

-means: Let the

L^{p}

-mean estimator, which constitutes the specific functional that estimates the

L^{p}

-mean of N independent and identically distributed random variables; then, (i) the expectation value of the

L^{p}

-mean estimator equals the mean of the distributions of the random variables; and (ii) the limit

N \to \infty

of the

L^{p}

-mean estimator also equals the mean of the distributions.

Keywords: expectation values; variance; optimization; fitting methods; Lp Norms; time series analysis

Share and Cite

MDPI and ACS Style

Livadiotis, G. On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means. Entropy 2017, 19, 217. https://doi.org/10.3390/e19050217

AMA Style

Livadiotis G. On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means. Entropy. 2017; 19(5):217. https://doi.org/10.3390/e19050217

Chicago/Turabian Style

Livadiotis, George. 2017. "On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means" Entropy 19, no. 5: 217. https://doi.org/10.3390/e19050217

APA Style

Livadiotis, G. (2017). On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means. Entropy, 19(5), 217. https://doi.org/10.3390/e19050217

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

On the Convergence and Law of Large Numbers for the Non-Euclidean L^p -Means

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI