Computing Higher Central Moments for Interval Data

Authors

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

Publication Date

6-2004

Comments

Technical Report: UTEP-CS-03-14b

Abstract

Higher central moments are very useful in statistical analysis: the third moment M3 characterizes asymmetry of the corresponding probability distribution, the fourth moment M4 describes the size of the distribution's tails, etc. When we know the exact values x1,...,xn, we can use the known formulas for computing the corresponding sample central moments. In many practical situations, however, we only know intervals [x1],...,[xn] of possible values of xi; in such situations, we want to know the range of possible values of Mm. In this paper, we propose algorithms that compute such ranges.