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HyperStar - Phase-type fitting made easy.

HyperStar is a tool for fitting phase-type distributions to data sets.

Phase-type distributions (often abbreviated as PH distributions) are a class of statistical distributions with attractive properties: hyper_small

  • Phase-type distributions can approximate any distribution with non-negative support arbitrarily closely. Therefore, they can be used to model a wide range of phenomena, including service-times, failure-processes, security incidents, and spatial distributions.

  • Phase-type distributions have closed-form expressions for the distribution function, density function, and moments and thus provide compact representations of empirical data

  • Phase-type distributions can be represented as Markov chains, which makes them suitable for use in analytical approaches to system evaluation, such as matrix-geometric methods.

  • Phase-type distributions can be used to efficiently generate random variates for simulation, thereby representing empirical phenomena in simulation studies.


The HyperStar tool was developed around the core idea of making phase-type fitting simple and user-friendly, in order to advance the use of phase-type distributions in a wide range of areas. Its major advantages include

  • A graphical user interface for exploration of the data and an intuitive method for parameterisation of the fitting algorithm.

  • A Beginners mode where the user can fit a phase-type distribution to a data set without any knowledge of the underlying theory of these distributions.

  • Good fitting results with little user interaction.

  • Support for the Hyper-Erlang distributions as well as other mixtures of distributions.

  • An Experts mode that allows fine-tuning of the fitting algorithms.

  • An interface to the Mathematica software package which enables the use of HyperStar as a graphical user-interface for fitting algorithms implemented in Mathematica. This feature supports the development of new phase-type fitting algorithms.

  • Support for various export formats of the fitted distributions, including support for the Libphprng/Butools package for random-variate generation.

  • A platform-independent Java implementation.


HyperStar is freely available for academic and private use, but we would be glad to hear from you if you use it (and what you use it for).

For commercial use, please contact either


Download the current version of HyperStar here:

Download the library for phase-type distributed random variates here:


  • Philipp Reinecke

  • Tilman Krauß

  • Katinka Wolter