Selecting Parameters of Phase Distributions: Combining Nonlinear Programming, Heuristics, and Erlang Distributions

Because of their denseness and tractability, phase (PH) distributions are widely used in probabilistic modeling. However, full exploitation of the favorable properties of PH distributions requires the ability to specify PH-distribution parameters to obtain adequate distribution approximations. We combine nonlinear-programming techniques and heuristics to select mixtures of Erlang distributions (a subset of the PH family) to approximate non-PH distributions. Heuristics are used to select the number of Erlang distributions mixed and the order of each mixed Erlang distribution, both of which have an important effect on the range of distribution properties that can be attained. Heuristics are also used for assigning initial values and bounds to the mixing probabilities and the means of the mixed Erlang distributions. Then nonlinear-programming methods are used to determine final values of these continuous parameters. Using a variety of criteria, we show that good fits can often be obtained with a moderate amo...