Population Variance under Interval Uncertainty: A New Algorithm

Authors

Evgeny Dantsin
Vladik Kreinovich, The University of Texas at El PasoFollow
Alexander Wolper
Gang Xiang

Publication Date

11-2005

Comments

UTEP-CS-05-28.

Published in Reliable Computing, 2006, Vol. 12, No. 4, pp. 273-280.

Abstract

In statistical analysis of measurement results, it is often beneficial to compute the range [V] of the population variance V when we only know the intervals [Xi-Di,Xi+Di] of possible values of xi. In general, this problem is NP-hard; a polynomial-time algorithm is known for the case when the measurements are sufficiently accurate, i.e., when |Xi-Xj| >= (D_i+D_j)/n for all i =/= j. In this paper, we show that we can efficiently compute [V} under a weaker (and more general) condition |Xi-Xj| >= |D_i-D_j|/n.