How to Define Relative Approximation Error of an Interval Estimate: A Proposal

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2012

Comments

Technical Report: UTEP-CS-12-37

Published in Applied Mathematical Sciences, 2013, Vol. 7, No. 5, pp. 211-216.

Abstract

The traditional definition of a relative approximation error of an estimate X as the ratio |X - x|/|x| does not work when the actual value x is 0. To avoid this problem, we propose a new definition |X - x|/|X|. We show how this definition can be naturally extended to the case when instead of a numerical estimate X, we have an interval estimate [x], i.e., an interval that is guaranteed to contain the actual (unknown) value x.