Frame theory in directional statistics

Martin Ehler; Jennifer Galanis

doi:10.1016/j.spl.2011.02.027

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arXiv · 1101.0122

Frame theory in directional statistics

Martin Ehler·Jennifer Galanis

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Abstract

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics with frame theory, we find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.

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Martin Ehler, Jennifer Galanis. 2010-12-30. Frame theory in directional statistics. https://doi.org/10.1016/j.spl.2011.02.027

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