Matching moments to phase distributions: density function shapes

We study density-function shapes of distributions selected by phase-distribution-selection methods developed in Johnson and Taaffe [2, 3]. In Johnson and Taaffe [2], analytic results for matching three moments to mixtures of two Erlang distributions of common order are presented. In Johnson and Taaffe [3], nonlinear programming methods are developed for matching three moments to mixtures of two Erlang distributions (not necessarily of the same order), real-parametered Coxian distributions with support on (0, ∞), and phase distributions with support on (0, ∞). In this paper, we investigate the effect of restricting selection to the above subsets of phase distributions. We also illustrate how to use the methods of Johnson and Taaffe [2, 3] to effect changes in density-function shapes.