Why 95% and Two Sigma? A Theoretical Justification for an Empirical Measurement Practice

Authors

Hung T. Nguyen
Vladik Kreinovich, The University of Texas at El PasoFollow
Chin-Wang Tao

Publication Date

7-2000

Comments

UTEP-CS-00-26a.

Proc. International Workshop on Intelligent Systems Resolutions: The 8th Bellman Continuum, Taipei, Taiwan, December 11-12, 2000, pp. 358-362.

Abstract

The probability p(k) that the value of a random variable is far away from the mean (e.g. further than k standard deviations away) is so small that this possibility can be often safely ignored. It is desirable to select k for which the dependence of the probability p(k) on the distribution is the smallest possible. Empirically, this dependence is the smallest for k between 1.5 and 2.5. In this paper, we give a theoretical explanation for this empirical result.