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.