Analysing the properties of a probability distribution is a question of general interest. In this paper we describe the properties of the matrix-exponential class of distributions, developing some properties for the discrete case and proving the closure properties, which for the case of phase-type distributions are extended to the matrix-exponential case, this not being an immediate consequence. Given the structure of this class of distributions, we were able to achieve the results in both

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... x and algorithmic form. These results can be used in stochastic modelling, and in the latter case, the model can be analysed in matrix and algorithmic form.