Bilateral phase type distributions

Soohan Ahn, V. Ramaswami

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A new class of probability distributions called "bilateral phase type distributions (BPH)" on (-∞, ∞) is defined as a generalization of the versatile class of phase type (PH) distributions on [0, ∞) introduced by Marcel F. Neuts. We derive the basic descriptors of such distributions in an algorithmically tractable manner and show that this class has many interesting closure properties and is dense in the class of all distributions on the real line. Based on the established versatility and tractability of phase type distributions, we believe that this class has high potential for general use in statistics, particularly to cover non-normal distributions, and also that its inherent connection to Markov chains may make it suitable for inference based on hidden Markov chain methods and MCMC type approaches.

Original languageEnglish
Pages (from-to)239-259
Number of pages21
JournalStochastic Models
Issue number2-3
StatePublished - 2005


  • Hidden markov models
  • Markov reward
  • Phase type models
  • Probability distribution


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