EM Estimation in Phase Type Models

Doctoral thesis, 1995

This thesis consists of four articles whose theme in common is the class of phase type distributions. In the first article an EM algorithm is presented to estimate the parameters of a phase type distribution of fixed order. Also, it is shown that the algorithm can be used to approximate other continuous distributions by phase type distributions. In article number two, the EM algorithm is adjusted to handle fitting of phase type distributions to samples containing right censored and/or interval censored observations. The third article deals with approximations of standard errors of identifiable functions (e.g. the distribution function at a fixed point) of a fitted phase type distribution. Standard error approximations are calculated both by using asymptotic theory and by using the jackknife technique. The two methods are compared and evaluated by simulations in several examples. The last article presents a parametric model for estimation of the relapse time of a disease in certain clinical trials. The model is a special phase type model where the state space of the underlying Markov process is split into two parts; the first set of states represents the patient still being healthy, a transition to a second set of states takes place when the patient get a relapse, and a transition to an absorbing state represents the patient getting symptoms of the disease.