Experimenting with the Coxian Phase-Type distribution to uncover suitable fits

Marshall and Zenga have a new paper in Methodology and Computing in Applied Probability. This considers the best approach to fitting Coxian phase-type distributions to fully observed survival or duration data. Several previous studies have shown that the EM algorithm, Nelder-Mead and quasi-Newton approaches give estimates that are highly dependent on initial values. In a series of simulations it is shown that the quasi-Newton algorithm is preferable to Nelder-Mead in converging to values closer to the true parameters. However, in the absence of a criterion for global convergence it still seems wise to consider several starting values to try to ensure a global rather than local optimum is obtained.