On properties of the phase-type mixed Poisson process and its applications to reliability shock modeling (Q2684950)

The authors study properties of the so-called Poisson phase-type process, a mixed non-homogeneous Poisson process with phase-type mixing distribution. Properties derived include the distribution, moments and moment generating function for the number of events up to time \(t\), the distribution of the inter-event times, and some stochastic ordering and ageing properties of this family of processes. These latter results are derived with the help of results on ordering and ageing properties of phase-type distributions, which may be of independent interest. As applications of this family of processes, the authors study various shock models in which the shocks arrive at the times of this Poisson phase-type process.