One approach to the moment-matching problem for phase distributions to restrict selection to an appropriate subset of phase distributions. The authors investigate the use of mixtures of Erlang distributions of common order to match moments feasible for distributions with support on [0,•). They show that, except for special cases, the first k (finite) moments of any nondegenerate distribution with support on [0,•) can be matched by a mixture of Erlang distributions of (sufficiently high) common order. Moreover, the authors show that any k-tuple of first k moments feasible for a mixture of n-stage Erlang distributions (En’s) is feasible for a mixture of ⌊k/2⌋+1 fewer En’s. The three-moment-matching problem is considered in detail. The set of pairs of second and third standardized moments feasible for mixtures of En’s is characterized. An analytic expression is derived for the minimum order, n such that a given set of first three moments is feasible for a mixture of En’s. Expressions are also given for the parameters of the unique mixture of two En’s that matches a feasible set of first three moments. Methods for implementation of these results are suggested and evaluated. In the present evaluation, the authors consider distributional properties such as dimension, numerical stability, and density-function shape.
