This paper describes a novel moment matching based fitting method for phase-type (PH) distributions. A special sub-class of phase-type distributions is introduced for the fitting, called generalized hyper-Erlang distributions. The user has to provide only two parameters: the number of moments to match, and the upper bound for the sum of the multiplicities of the eigenvalues of the distribution, which is related to the maximal size of the resulting PH distribution. Given these two parameters, our method obtains all PH distributions that match the target moments and have a Markovian representation up to the given size. From this set of PH distributions the best one can be selected according to any distance function
