dcor: distance correlation and energy statistics in Python.

## dcor

dcor: distance correlation and energy statistics in Python.

E-statistics are functions of distances between statistical observations in metric spaces.

Distance covariance and distance correlation are dependency measures between random vectors introduced in [SRB07] with a simple E-statistic estimator.

This package offers functions for calculating several E-statistics such as:

• Estimator of the energy distance [SR13].

• Biased and unbiased estimators of distance covariance and distance correlation [SRB07].

• Estimators of the partial distance covariance and partial distance covariance [SR14].

It also provides tests based on these E-statistics:

• Test of homogeneity based on the energy distance.

• Test of independence based on distance covariance.

## Installation

dcor is on PyPi and can be installed using pip:

pip install dcor

It is also available for conda using the conda-forge channel:

conda install -c conda-forge dcor

Previous versions of the package were in the vnmabus channel. This channel will not be updated with new releases, and users are recommended to use the conda-forge channel.

### Requirements

dcor is available in Python 3.8 or above in all operating systems. The package dcor depends on the following libraries:

• numpy

• numba >= 0.51

• scipy

• joblib

## References

[SR13]

Gábor J. Székely and Maria L. Rizzo. Energy statistics: a class of statistics based on distances. Journal of Statistical Planning and Inference, 143(8):1249 – 1272, 2013. URL: http://www.sciencedirect.com/science/article/pii/S0378375813000633, doi:10.1016/j.jspi.2013.03.018.

[SR14]

Gábor J. Székely and Maria L. Rizzo. Partial distance correlation with methods for dissimilarities. The Annals of Statistics, 42(6):2382–2412, 12 2014. doi:10.1214/14-AOS1255.

[SRB07] (1,2)

Gábor J. Székely, Maria L. Rizzo, and Nail K. Bakirov. Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6):2769–2794, 12 2007. doi:10.1214/009053607000000505.

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