Closed form of PH-distribution

In this paper a new approach of Jordan canonical formulation for analysis of a PH-subgenerator is proposed. Based on the new method, this paper shows that if all eigenvalues of a PH-subgenerator are real then the closed form of the PH-distribution is a linear combination of Erlang distributions, while if the subgenerator has complex eigenvalues then the closed form of the PH-distribution is no longer such a simple form but more complex form that includes trigonometric functions in addition to a linear combination of Erlang distributions. This paper also shows that the dominant parameter for degree of a PH-distribution is not the size but the degree of minimal polynomial of the PH-subgenerator.