Asymmetrical uncertainties

Abstract

In several disciplines, measurement results occasionally are expressed using coverage intervals that are asymmetric relative to the measured value. The conventional treatment of such results, when there is the need to propagate their uncertainties to derivative quantities, is to replace the asymmetric uncertainties by 'symmetrized' versions thereof. We show that such simplification is unnecessary, illustrate how asymmetry may be modeled and recognized explicitly, and propagated using standard Monte Carlo methods. We present three distributions (Fechner, skew-normal, and generalized extreme value), among many available alternatives, that can be used as models for asymmetric uncertainties associated with scalar input quantities, in the context of the measurement model considered in the GUM. We provide an example where such uncertainties are propagated to the uncertainty of a ratio of mass fractions. We also show how a similar, model-based approach can be used in the context of data reductions from interlaboratory studies and other consensus building exercises where the reported uncertainties are expressed asymmetrically, illustrating the approach to obtain consensus estimates of the absorption cross-section of ozone, and of the distance to galaxy M83 in the Virgo cluster.