Frame theory in directional statistics |
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| Authors: | Martin Ehler Jennifer Galanis |
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| Affiliation: | a National Institutes of Health, National Institute of Child Health and Human Development, Section on Medical Biophysics, Bethesda, MD 20892, United Statesb University of Maryland, Department of Mathematics, Norbert Wiener Center, College Park, MD 20742, United Statesc Institute of Chemistry and The Fritz Haber Center, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel |
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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. To predict these distributions, we merge directional statistics with frame theory and 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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| Keywords: | 42C15 62H11 62P10 |
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