This paper develops algorithms for finding Coxian generators to phase‐type (PH)‐majorize a PH‐generator T with only real eigenvalues. In the first part of this paper, we investigate matrices S and P satisfying TP = PS and P
e = e. Conditions on T are identified for S to be an ordered Coxian generator and for P to be nonnegative, which consequently implies that S
PH‐majorizes T. It is shown that every PH‐generator with only real eigenvalues is PH‐majorized by some Coxian generator. In the second part of this paper, the results on S and P and the conditions on T are used to develop efficient algorithms for Coxianization of PH‐generators. Numerical examples are presented for a comparison between the developed algorithms.
