Energy distance

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. (C) 2015 Wiley Periodicals, Inc.