**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*where

_{1},x_{2})*x*would be an arbitrary Gamma variate [with a given variance] and

_{1}*x*conditional on

_{2}*x*would be a Gamma variate with parameters specified by the covariance matrix. Which does not extend nicely to larger dimensions.

_{1}