Matching moments to phase distributions: Nonlinear programming approaches

The authors present a nonlinear programming (NLP) approach to the problem of matching three moments to phase distributions. They first discuss the formulation and implementation of a general NLP problem and then consider NLP problems for searching over two families of phase distributions: mixtures of two Erlang distributions and real-parametered continuous Coxian distributions. Restricting the search to select from a subset of phase distributions allows us to greatly simplify the NLP problem, resulting in more efficient and predictable search procedures. Conversely, the restriction also reduces the variety of distributions the search algorithm can select. Tradeoffs between the formulations and possible refinements and extensions are discussed.