Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms

13 years 10 months ago

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In statistical analysis of measurement results, it is often necessary to compute the range [V , V ] of the population variance V = 1 n · n i=1 (xi −E)2 (where E = 1 n · n i=1 xi) when we only know the intervals [xi − ∆i, xi + ∆i] of possible values of the xi. While V can be computed eﬃciently, the problem of computing V is, in general, NP-hard. In our previous paper, we showed that in a practically important case, we can use constraints techniques to compute V in time O(n · log(n)). In this paper, we provide new algorithms that compute V and, for the above case, V in linear time O(n). Similar linear-time algorithms are described for computing the range of the entropy S = − n i=1 pi · log(pi) when we only know the intervals pi = [pi , pi] of possible values of probabilities pi. 1 Computing Population Variance under Interval Uncertainty: Formulation of the Problem Once we have n measurement results x1, . . . , xn, the traditional statistical analysis starts with computin...

Gang Xiang, Martine Ceberio, Vladik Kreinovich

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