## Departmental Technical Reports (CS)

6-2011

#### Abstract

In many practical situations, it is important to estimate themean E and the variance V from the sample valuesx1, ..., xn. Usually, in statistics,we consider the case when the parameters like E and V do not change with timeand when the sample values xi are known exactly. Inpractice, the values xicome from measurements, andmeasurements are never 100% accurate. In many cases, we onlyknow the upper bound Di on the measurement error. Inthis case, once we know the measured value Xi, wecan conclude that the actual (unknown) value xi belongs tothe interval [Xi - Di, Xi +Di]. Different values xi 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.

COinS
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