# Software

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## Software

### Moore Rayleigh test

The Moore-Rayleigh test is a nonparametric test for spherical symmetry. In two dimensions it is known as the Moore test. Its generalization to three or more dimensions has been introduced in the technical report MI-2009-05. In three dimensions, the Moore-Rayleigh test statistic can be efficiently evaluated (with high precision) from a combinatorial sum representation. This allows to run a large number of tests in a short time, as needed, e.g., in neuroscientific applications.

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• Todo: make C++ version available

### Dissimilarity analysis of time series by Wasserstein distances

Wasserstein distances are a class of distances between probability measures. In the discrete case, the latter correspond to (weighted) point sets. Alternatively, time series can be considered such a point set, and the Wasserstein distance quantifies the “distance” between two such series. Delay embedding of time series results in multi-dimensional point sets, and also for these the Wasserstein distances provide meaningful distance measures.

• Software provided:
• wassersteinCC: a command-line utility that calculates Wasserstein distances for two ASCII input files. Included is also a (rudimentary) Matlab interface
• dts: a comprehensive collection of routines for the statistical software environment R. Provides facilities to calculate Wasserstein distances and to analyse the resulting distance matrices (LDA/CCA classification, permutation tests, cross-validation of MDS representations). Additionally, facilities for (multi-exponent) detrended fluctuation analysis (DFA) is provided, as well as routines for fitting power-law and log-normal distributions. (…coming soon…)