Title: Phase type process
Authors: Paula Bouzas - University of Granada (Spain) [presenting]
Nuria Ruiz-Fuentes - University of Jaen (Spain)
Carmen Montes-Gijon - University of Granada (Spain)
Abstract: Non-negative valued stochastic processes are often observed when studying real phenomena; consequently, modeling these processes is an interesting issue. Linear combinations of exponentials, gamma or Weibull distributions are commonly encountered in the literature in order to model them. Based on the fact that the most general model for a non-negative valued random variable is the phase type distribution, a new non-negative stochastic model is proposed. The phase type process is defined as a doubly stochastic process whose marginals are phase type distributions with random parameters. Survival, reliability and queuing theory or counting processes are fields in which non-negative stochastic processes play an important role. As an example, a compound Cox process whose intensity is a phase type process is considered. This counting process emerges as especially flexible and general. After this description, a simulation study is presented.