Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions. The name energy derives from Newton's gravitational potential energy, and there is an elegant relation to the notion of potential energy between statistical observations. Energy statistics are functions of distances between statistical observations in metric spaces. The authors hope this book will spark the interest of most statisticians who so far have not explored E-statistics and would like to apply these new methods using R. The Energy of Data and Distance Correlation is intended for teachers and students looking for dedicated material on energy statistics, but can serve as a supplement to a wide range of courses and areas, such as Monte Carlo methods, U-statistics or V-statistics, measures of multivariate dependence, goodness-of-fit tests, nonparametric methods and distance based methods.

•E-statistics provides powerful methods to deal with problems in multivariate inference and analysis.

•Methods are implemented in R, and readers can immediately apply them using the freely available energy package for R.

•The proposed book will provide an overview of the existing state-of-the-art in development of energy statistics and an overview of applications.

•Background and literature review is valuable for anyone considering further research or application in energy statistics.

chapter I|180 pages

The Energy of Data

chapter 21|10 pages


chapter 2|10 pages


chapter 3|22 pages

Energy Distance

chapter 4|14 pages

Introduction to Energy Inference

chapter 5|24 pages


chapter 6|16 pages

Testing Multivariate Normality

chapter 7|22 pages

Eigenvalues for One-Sample E-Statistics

chapter 8|10 pages

Generalized Goodness-of-Fit

chapter 9|24 pages

Multi-sample Energy Statistics

chapter 10|26 pages

Energy in Metric Spaces and Other Distances

chapter II|226 pages

Distance Correlation and Dependence

chapter 12|22 pages

Distance Correlation

chapter 13|18 pages

Testing Independence

chapter 14|20 pages

Applications and Extensions

chapter 15|12 pages

Brownian Distance Covariance

chapter 16|20 pages

U-statistics and Unbiased dCov2

chapter 17|24 pages

Partial Distance Correlation

chapter 18|10 pages

The Numerical Value of dCor

chapter 20|20 pages

Computational Algorithms

chapter 21|10 pages

Time Series and Distance Correlation

chapter 22|20 pages

Axioms of Dependence Measures

chapter 23|12 pages

Earth Mover's Correlation