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This report presents a novel method of teaching curvature measures via simple 2D examples using the elementary formulae for curvature encountered by undergraduate students. Using this procedure students can verify algebraically and numerically the invariance of intrinsic curvature and corroborate the best parameterisation by examination of parameter effects curvature, again mathematically and empirically. For serious users of curvature measures, this elementary exposition also reconciles the general definition of 'statistical curvature' coined by Efron (1975), with the approach of Amari (1990), albeit for the exponential connection only. |
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