Estimating Mean and Variance under Interval Uncertainty: Dynamic Case

Authors

Rafik Aliev, Azerbaijan State Oil Academy
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2011

Comments

Technical Report: UTEP-CS-11-29

Published in Proceedings of the 2011 Sixth International Conference on Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control ICSCCW'2011, Antalya, Turkey, September 1-2, 2011, pp. 85-93.

Abstract

In many practical situations, it is important to estimate themean E and the variance V from the sample valuesx₁, ..., x_n. Usually, in statistics,we consider the case when the parameters like E and V do not change with timeand when the sample values x_i are known exactly. Inpractice, the values x_icome from measurements, andmeasurements are never 100% accurate. In many cases, we onlyknow the upper bound D_i on the measurement error. Inthis case, once we know the measured value X_i, wecan conclude that the actual (unknown) value x_i belongs tothe interval [X_i - D_i, X_i +D_i]. Different values x_i from these intervalslead, in general, to different values of E and V. It istherefore desirable to find the ranges [E] and [V]of all possible values of E and V. While this problem is,in general, NP-hard, in many practical situations, there existefficient algorithms for computing such ranges.

In practice, processes are dynamic. As a result, reasonableestimates for E and V assign more weight to more recentmeasurements and less weight to the past ones. In this paper,we extend known algorithms for computing the ranges [E] and [V]to such dynamic estimates.