Evaluating expanded uncertainty in measurement with a fitted distribution

Abstract

It is recommended in the internationally adopted standard GUM that the measurement result of a measurand Y , determined from input quantities through a known functional relationship, should be reported as an uncertainty interval with a specific level of confidence. The uncertainty intervals discussed in GUM are evaluated by assuming that the measurements of Y follow a normal or t distribution. However, in practice, the resulting measurements of Y tend to follow an asymmetric distribution. This communication reviews some generalized univariate distributions that can be fitted to the measurements of Y based on its shape in terms of its coefficients of skewness and kurtosis. The uncertainty interval of the measurand is then evaluated from the fitted distribution. Examples are given to illustrate the use of these distributions in evaluating the expanded uncertainty in measurement.

Representing Monte Carlo output distributions for transferability in uncertainty analysis: modelling with quantile functions

“…This assumption and the corresponding assumption that an ELD provides a good approximation could be examined by comparing the fifth and sixth moments of the fitted distributions to the exact fifth and sixth moments. The distributions studied by Sim and Lim [16] might also be fitted and examined in the same way. We might then choose one of the intervals or form an 14 Provided that the extreme values of this sample do not fall outside the bounds of the exact distribution, this random sample from the approximating distribution can also be legitimately regarded as an 'approximately random' sample from the exact distribution.…”

“…The term 'the generalized lambda distribution' has been used to refer to the first of these two other distributions, but has also been used to refer to both without explicit recognition of the fact that they describe different families. The second of these two distributions has recently been studied by Sim and Lim [16] for use in obtaining coverage intervals from moments. Ramberg [9, equation ( 4)] considered a five-parameter generalization with quantile function of the form…”

“…The values of a, c and d are then given by ( 14)- (16). A suitable choice is (p 1 , p 2 , p 3 , p 4 ) = (0.025, 0.25, 0.75, 0.975), in which case ( 17) is applicable with p 1 = 0.025 and p 2 = 0.25.…”

Gas Sensor Array Dynamic Measurement Uncertainty Evaluation and Optimization Algorithm

“…However, there are few papers on the dynamic uncertainty of sensor arrays. In the papers in [19]- [21], the uncertainty of the generalized Lambda distribution of expressions is described, but the proposed algorithm is not suitable for the estimation of measurement uncertainty of MOS gas sensor arrays. The paper in [18], [22], and [23] discussed the uncertainty assessment in indirect measurements, where the main concern is the measurement model.…”