Applying the Monte Carlo method for propagation of measurement uncertainty described in the GUM Supplement 1, when the input quantities are correlated, involves the specification of a joint probability distribution for these quantities. In practice, however, all that typically is available are probability distributions for the individual input quantities (their marginal distributions), and estimates of the correlations between them. Therefore, a method is needed to manufacture that joint distribution. However, there are infinitely many joint distributions that are consistent with given marginal distributions and correlations. This paper explains how copulas may be used to manufacture joint probability distributions consistent with given margins and correlations, illustrates such use in the context of example H.2 from the GUM, and discusses the choice of copula.
uncertainty analysis, propagation of distributions, GUM Supplement 1, Monte Carlo method, parametric bootstrap, copula, joint probability distribution, multivariate probability distribution, correlation supplicant, closest correlation matrix.