Computing Variance for Interval Data is NP-Hard

Authors

Scott Ferson
Lev Ginzburg
Vladik Kreinovich, The University of Texas at El PasoFollow
Luc Longpre, The University of Texas at El PasoFollow
Monica Aviles

Publication Date

4-2002

Comments

UTEP-CS-02-13b.

Published in ACM SIGACT News, 2002, Vol. 33, No. 2, pp. 108-118.

Abstract

When we have only interval ranges [xi-,xi+] of sample values x1,...,xn, what is the interval [V-,V+] of possible values for the variance V of these values? We prove that the problem of computing the upper bound V+ is NP-hard. We provide a feasible (quadratic time) algorithm for computing the lower bound V- on the variance of interval data. We also provide a feasible algorithm that computes V+ under reasonable easily verifiable conditions.