Approximating matrix-exponential distributions by global randomization

Based on the general concept of randomization, we develop linear-algebraic approximations for continuous probability distributions that involve the exponential of a matrix in their definitions, such as phase types and matrixexponential distributions. The approximations themselves result in proper probability distributions. For such a global randomization with the Erlangdistribution, we show that the sequences of true and consistent distribution and density functions converge uniformly on . Furthermore, we study the approximation errors in terms of the power moments and the coefficients of the Taylor series, from which the accuracy of the approximations can be determined apriori. Numerical experiments demonstrate the feasibility of the presented randomization technique – also in comparison with uniformization.