# Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements

Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of... When we have n results x 1,...,x n of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals x i of possible values of x 1 In such situations, for different possible values x i∈ x i, we get different values of the variance. We must therefore find the range V of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval V in quadratic time O(n2). In this paper, we describe a new algorithm for computing V that requires time O(n log(n)) (which is much faster than O(n 2)). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements

, Volume 12 (1) – Jan 1, 2006
6 pages

/lp/springer_journal/fast-algorithm-for-computing-the-upper-endpoint-of-sample-variance-for-i3p1Kem0XQ
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-2965-8
Publisher site
See Article on Publisher Site

### Abstract

When we have n results x 1,...,x n of repeated measurement of the same quantity, the traditional statistical approach usually starts with computing their sample average E and their sample variance V. Often, due to the inevitable measurement uncertainty, we do not know the exact values of the quantities, we only know the intervals x i of possible values of x 1 In such situations, for different possible values x i∈ x i, we get different values of the variance. We must therefore find the range V of possible values of V. It is known that in general, this problem is NP-hard. For the case when the measurements are sufficiently accurate (in some precise sense), it is known that we can compute the interval V in quadratic time O(n2). In this paper, we describe a new algorithm for computing V that requires time O(n log(n)) (which is much faster than O(n 2)).

### Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

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