MEASURES OF GLOBAL RELATIVE CURVATURE.

Abstract

The descriptive problem is considered in determining to what extent a convex regression function appears to have smooth change in slope rather than abrupt changes as typified by broken lines. An index of relative curvature is defined which assigns large values to functions having smooth first derivative and which is zero for broken lines. Discrete approximations to this index are considered, depending only on knowledge of the regression function at a finite set of points. Values of these indices are calculated for convex functions obtained from least squares regression fits in models having only the restriction of concavity. A Monte Carlo experiment was conducted to determine the variability of these discrete indices and some numerical results are presented. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 20, 1967
Accession Number
AD0660682

Entities

People

  • Paul I. Feder

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Curvature
  • Curves (Geometry)
  • Differential Geometry
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Computational Modeling and Simulation
  • Theoretical Analysis.