Implementation of the characteristic functions approach to measurement uncertainty evaluation

Probability distributions suitable for modelling measurements and determining their uncertainties are usually based on a standard approximation approach as described in GUM, i.e. the GUM uncertainty framework (GUF), using the law of uncertainty propagation (also known as the delta method) or a more accurate method based on the law of probability propagation calculated using the Monte Carlo method (MCM). As an alternative to GUF and MCM, we present a characteristic function approach (CFA), which is suitable for determining measurement uncertainties by using the exact probability distribution of a measured quantity in linear measurement models by inverting the associated characteristic function (CF), which is defined as a Fourier transform of the probability density function (PDF). In this paper, we present the current state of the MATLAB implementation of the characteristic function approach (the toolbox CharFunTool) and illustrate the use and applicability of the CFA for determining the distribution and uncertainty evaluation with a simple example. The proposed approach is compared with GUM, MCM and the kurtosis uncertainty method (KUM).