# Generate correlated samples from elicited marginal distributions using a multivariate normal copula Takes elicited marginal distributions and elicited concordance probabilities: pairwise probabilities of two uncertain quantities being greater than their medians, and generates a correlated sample, assuming the elicited marginal distributions and a multivariate normal copula. A vignette explaining this method is available at [https://oakleyj.github.io/SHELF/Multivariate-normal-copula.html](https://oakleyj.github.io/SHELF/Multivariate-normal-copula.html) ```r copulaSample(..., cp, n, d = NULL, ex = 1) ``` ## Arguments - `...`: A list of objects of class `elicitation`. command, one per marginal distribution, separated by commas. - `cp`: A matrix of pairwise concordance probabilities, with element i,j the elicited probability P(X_i > m_i, X_j > m_j or X_i < m_i, X_j < m_j), where m_i and m_j are the elicited medians of the uncertain quantities X_i and X_j. Only the upper triangular elements in the matrix need to be specified; the remaining elements can be set at 0. - `n`: The sample size to be generated - `d`: A vector of distributions to be used for each elicited quantity: a string with elements chosen from `"normal", "t", "gamma", "lognormal", "logt", "beta", "mirrorgamma","mirrorlognormal", "mirrorlogt"`. The default is to use the best fitting distribution in each case. - `ex`: If separate judgements have been elicited from multiple experts and stored in the `elicitation` objects, use this argument to select a single expert's judgements for sampling. Note that this function will not simultaneously generate samples for all experts. ## Returns A matrix of sampled values, one row per sample. ## Examples ```r ## Not run: p1 <- c(0.25, 0.5, 0.75) v1 <- c(0.5, 0.55, 0.6) v2 <- c(0.22, 0.3, 0.35) v3 <- c(0.11, 0.15, 0.2) myfit1 <- fitdist(v1, p1, 0, 1) myfit2 <- fitdist(v2, p1, 0, 1) myfit3 <- fitdist(v3, p1, 0, 1) quad.probs <- matrix(0, 3, 3) quad.probs[1, 2] <- 0.4 quad.probs[1, 3] <- 0.4 quad.probs[2, 3] <- 0.3 copulaSample(myfit1, myfit2, myfit3, cp=quad.probs, n=100, d=NULL) ## End(Not run) ``` ## Author(s) Jeremy Oakley [j.oakley@sheffield.ac.uk](mailto:j.oakley@sheffield.ac.uk)

copulaSample function