To predict values of future quantities, we apply algorithms to the current and past measurement results. Because of the measurement errors and model inaccuracy, the resulting estimates are, in general, different from the desired values of the corresponding quantities. There exist methods for estimating this difference, but these methods have been mainly developed for the two extreme cases: the case when we know the exact probability distributions of all the measurement errors and the interval case, when we only know the bounds on the measurement errors. In practice, we often have some partial information about the probability distributions which goes beyond these bounds. In this paper, we show how the existing methods of estimating uncertainty can be extended to this generic case.