A Benchmark for PH Estimation Algorithms: Results for Acyclic-PH

Distribution functions that can be expressed as exponential polynomials have useful computational properties in applied stochastic modeling and have gained widespread acceptance in recent years. Nevertheless, the implementation of efficient numerical procedures for estimating the distribution parameters remains an open problem that limits the use of this class of distributions in applications. The difficulty of the fitting problem is largely related to the non-linearity of the model and to the number of the parameters to be estimated. Many attempts have been presented in the literature. However, the lack of accepted and standardized test examples makes it difficult to establish a comparative merit among the various approaches. This paper proposes a benchmark based on the workshop on Fitting phase type distributions, organized by S. Asmussen in February 1991. It also presents the results obtained by applying the Maximum Likelihood (ML) estimation procedure to the canonical representation of Acyclic Phase Type (APH) distributions.