TY - BOOK
T1 - Statistical Curvature in Two Dimensions
T2 - A Teaching Application
AU - Ellem, Bernard
AU - Thomas, Kylie
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
KW - Statistics
M3 - Report
T3 - Research and Technical Reports
BT - Statistical Curvature in Two Dimensions
PB - University of New England, School of Mathematics, Statistics and Computer Science
CY - Armidale, Australia
ER -