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Distributions de type phase. Tutorial. (Distributions of phase type. Tutorial). (French) Zbl 0696.60024
This is a tutorial on phase-type distributions, defined as absorption times for Markov processes with finitely many states. This class is of paramount importance in modern applied probability as generalization of the exponential distributions (other examples are Erlang and hyperexponential distributions and a large class of distributions with a rational Laplace transform), and the theory and its applications has been developed mainly by Neuts and his collaborators since 1975. Elementary analytical properties are discussed as well as closure properties, and applications to renewal theory, order statistics and queueing are outlined.
Reviewer: S.Asmussen

60E99 Distribution theory
60K05 Renewal theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
62G30 Order statistics; empirical distribution functions