A closure characterisation of phase-type distributions Journal Article

Overview

abstract

• We characterise the classes of continuous and discrete phase-type distributions in the following way. They are known to be closed under convolutions, mixtures, and the unary ‘geometric mixture' operation. We show that the continuous class is the smallest family of distributions that is closed under these operations and contains all exponential distributions and the point mass at zero. An analogous result holds for the discrete class.We also show that discrete phase-type distributions can be regarded as ℝ+-rational sequences, in the sense of automata theory. This allows us to view our characterisation of them as a corollary of the Kleene–Schützenberger theorem on the behavior of finite automata. We prove moreover that any summable ℝ+-rational sequence is proportional to a discrete phase-type distribution.

CU Boulder Authors

• Maier, Robert S

publication date

• March 1, 1992

Date in CU Experts

• March 4, 2026 2:25 AM

Full Author List

• Maier RS; O'Cinneide CA

author count

• 2

published in

• Journal of Applied Probability  Journal

Other Profiles

International Standard Serial Number (ISSN)

• 0021-9002

Electronic International Standard Serial Number (EISSN)

• 1475-6072

Digital Object Identifier (DOI)

• https://doi.org/10.2307/3214794

Additional Document Info

start page

• 92

end page

• 103

volume

• 29

issue

• 1