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Fast algorithm for computing the upper endpoint of sample variance for interval data: case of sufficiently accurate measurements
 Reliable Computing
, 2006
"... When we have n results x1,..., xn 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 quantiti ..."
Abstract

Cited by 12 (7 self)
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When we have n results x1,..., xn 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 xi of possible values of xi. In such situations, for different possible values xi ∈ xi, 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 NPhard. 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(n 2). 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)). 1
Applicationmotivated combinations of fuzzy, interval, and probability approaches, and their use in geoinformatics, bioinformatics, and engineering
 INT. J. AUTOMATION AND CONTROL
, 2007
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Abstract
"... This paper addresses the problem of market risk management for a company in the electricity industry. When dealing with corporate volumetric exposure, there is a need for a methodology that helps to manage the aggregate risks in energy markets. The originality of the approach presented lies in the u ..."
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This paper addresses the problem of market risk management for a company in the electricity industry. When dealing with corporate volumetric exposure, there is a need for a methodology that helps to manage the aggregate risks in energy markets. The originality of the approach presented lies in the use of intervals to formulate a specific portfolio optimization problem under stochastic dominance constraints.