**T**his is the question I posted this morning on StackOverflow, following an exchange two days ago with a user who could not see why the linear transform of a log-normal vector *X*,

**Y** = μ + Σ **X**

could lead to negative components in *Y*…. After searching a little while, I could not think of a joint distribution on the positive k-dimensional quadrant where I could specify the covariance matrix in advance. Except for a pedestrian construction of *(x*_{1},x_{2}) where *x*_{1} would be an arbitrary Gamma variate [with a given variance] and *x*_{2} conditional on *x*_{1} would be a Gamma variate with parameters specified by the covariance matrix. Which does not extend nicely to larger dimensions.

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