In this paper, we study the approximation of matrix-exponential distributions by Coxian distributions. Based on the spectral polynomial algorithm, we develop an algorithm for computing Coxian representations of Coxian distributions that are approximations of matrix-exponential distributions. As a specialization, we show that phase-type (PH) distributions can be approximated by Coxian distributions. We also show that any phase-type generator with only real eigenvalues is PH-majorized by ordered Coxian generators. Consequently, the algorithm is modified for computing ordered Coxian representations of any phase-type distribution whose Laplace-Stieltjes transform has only real poles. Numerical examples are presented to show the efficiency of the algorithm and the accuracy of the Coxian approximations.
Keywords: Matrix-exponential distribution, Coxian distribution, phase-type distribution, matrix analytic methods, Perron-Frobenius theory
Mathematics subject classification (2000): Primary 60A99, Secondary
15A18