Approximation of continuous distribution via the generalized Erlang distribution

In this paper, we study the approximation of a given probability distribution function by the generalized Erlang distribution (GED), which is a Phase-type Distribution (PH-D). In the method of moment we search equating the moments of a given probability distribution function and the moments of the GED which will approximate it. We will show conditions under which the approximation is feasible and will present a mathematical programming approach when the method of equating moments fails. The performance of this method is illustrated by numerical examples.