On the use of functional calculus for phase-type and related distributions

Mogens Bladt, Azucena Campillo Navarro, Bo Friis Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review


The area of phase-type distributions is renowned for its ability to obtain closed form formulas or algorithmically exact solutions to many complex stochastic models. The method of functional calculus will provide an additional tool along these lines for establishing results in terms of functions of matrices. Functional calculus, which is a branch of operator theory frequently associated with complex analysis, can be applied to phase-type and matrix-exponential distributions in a rather straightforward way. In this article we provide a number of examples of how to execute the formal arguments.
Original languageEnglish
JournalStochastic Models
Issue number1
Pages (from-to)1-19
Publication statusPublished - 2016


  • Complex analysis
  • Functional calculus
  • Matrix-exponential
  • Mellin transform
  • Phase-type distributions

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