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 matrix 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.
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