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Energy distance

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Energy distance is a metric that measures the distance between the distributions of random vectors. Energy distance is zero if and only if the distributions are identical, thus it characterizes equality of distributions and provides a theoretical foundation for statistical inference and analysis. Energy statistics are functions of distances between observations in metric spaces. As a statistic, energy distance can be applied to measure the difference between a sample and a hypothesized distribution or the difference between two or more samples in arbitrary, not necessarily equal dimensions. The name energy is inspired by the close analogy with Newton's gravitational potential energy. Applications include testing independence by distance covariance, goodness‐of‐fit, nonparametric tests for equality of distributions and extension of analysis of variance, generalizations of clustering algorithms, change point analysis, feature selection, and more. WIREs Comput Stat 2016, 8:27–38. doi: 10.1002/wics.1375 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Replicates generated under the null hypothesis in a test of multivariate normality for the iris setosa data. The test statistic ℰn,d of the observed iris sample is located by the black dot.
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Statistical and Graphical Methods of Data Analysis > Multivariate Analysis
Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

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