Skip to Content

Expanded uncertainty for complex quantities

Expanded uncertainty regions for complex quantities

B D Hall

Metrologia 2013, 50, 490-498


The expanded measurement uncertainty of a complex quantity is a region in the complex plane surrounding the measured value. This paper considers different shaped uncertainty regions in the form of ellipses, circles, rectangles and parallelograms. The different types of region are compared, under a variety of measurement error conditions, with regard to coverage probability and relative area. Elliptical confidence regions are commonly used in multivariate statistics. However, this shape has not been adopted widely in metrology, perhaps because there is no simple way to report the extent of an elliptical region. The other shapes considered are easier to use. Unfortunately, the coverage probability of circular uncertainty regions is found to be sensitive to both the form of the distribution of measurement errors and to the number of degrees of freedom, making this shape a poor choice. Parallelograms and rectangles both performed well, with parallelograms giving the best results overall.

Full text >>>