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https://hdl.handle.net/1959.11/4771| Title: | Statistical Curvature in Two Dimensions: A Teaching Application | Contributor(s): | Ellem, Bernard (author); Thomas, Kylie (author) | Publication Date: | 2005 | Handle Link: | https://hdl.handle.net/1959.11/4771 | Abstract: | 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. | Publication Type: | Report | Publisher: | University of New England, School of Mathematics, Statistics and Computer Science | Place of Publication: | Armidale, Australia | Fields of Research (FoR) 2008: | 010499 Statistics not elsewhere classified | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | HERDC Category Description: | R1 Report | Series Name: | Research and Technical Reports |
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| Appears in Collections: | Report |
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