Acyclic Discrete Phase Type Distributions: Part 1: Properties and Canonical Forms
نویسندگان
چکیده
The main goal of this paper is to derive properties about Discrete Phase Type (DPH) distributions and to provide results which make convenient their use in the approximate analysis of discrete state non-Markovian stochastic systems. To this end, similarities and di erences between DPH and Continuous Phase Type (CPH) distributions are investigated. An immediate di erence is that DPH distributions can represent in an exact way a number of distributions with nite support, like the deterministic. A minimal representation, called canonical form, for the subclass of Acyclic Discrete Phase Type distributions (ADPH) is provided. It is then shown that below a given order (that is a function of the expected value) the minimal coe cient of variation of the ADPH family is always less than the minimal coe cient of variation of the CPH family.
منابع مشابه
Classification and properties of acyclic discrete phase-type distributions based on geometric and shifted geometric distributions
Acyclic phase-type distributions form a versatile model, serving as approximations to many probability distributions in various circumstances. They exhibit special properties and characteristics that usually make their applications attractive. Compared to acyclic continuous phase-type (ACPH) distributions, acyclic discrete phase-type (ADPH) distributions and their subclasses (ADPH family) have ...
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