Calculation of the expanded uncertainty for large uncertainties using the lognormal distribution

For large uncertainties, calculating the expanded uncertainty using a normal distribution for the values of the measurand can lead to negative values for the lower limit of the expanded uncertainty and unrealistic large values for the upper limit, when the relative uncertainty is constant over wide concentration range. Using the lognormal distribution overcomes these problems and is particularly important when the relative uncertainty is larger than 10%; below this value, both distributions give almost identical results. The use of the lognormal distribution can be appropriate when the model equation for the derivation of the value of the measurand consists of products of input quantities, with positive values. Most measurement results are given as a mean and a relative uncertainty, and the purpose of this paper is to show how, for a lognormal distribution, the expanded uncertainty can be derived directly from these two parameters.