Abstract
The Laplace–Stieltjes transform of a matrix-exponential (ME) distribution is a rational function where at least one of its poles of maximal real part is real and negative. The coefficients of the numerator polynomial, however, are more difficult to characterise. It is known that they are contained in a bounded convex set that is the intersection of an uncountably infinite number of linear half-spaces. In order to determine whether a given vector of numerator coefficients is contained in this set (i.e. the vector corresponds to an ME distribution) we present a semi-infinite programming algorithm that minimises a convex distance function over the set. In addition, in the event that the given vector does not correspond to an ME distribution, the algorithm returns a closest vector which does correspond to one.
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