Ideally, the output of one calculation of measurement uncertainty should be usable as an input to another calculation. This paper describes (i) how the output distribution of a Monte Carlo (MC) evaluation of uncertainty can be summarized for use in another analysis and (ii) how a general probability distribution can be summarized for efficient use as an MC input distribution. The principal technique discussed involves fitting an asymmetric form of 'lambda distribution' to the summarizing data. This distribution is defined by the inverse of its distribution function, so the generation of random samples from this distribution is straightforward.

The inverse of the distribution function is known as the 'quantile function'. The principle advocated is that of working with distributions with convenient quantile functions instead of distributions with convenient probability density functions. This principle is applicable whether the distributions represent sampling distributions, as in frequentist statistics, or patterns of belief, as in Bayesian statistics.