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 ...
متن کاملAcyclic Discrete Phase Type Distributions. Part 2: A Parameter Estimation Algorithm
In Part 1 of this paper, the properties of Discrete Phase Type (DPH) distributions have been investigated, which make the use of this class of distributions very convenient in the approximate analysis of discrete state stochastic systems. In particular, a minimal representation, called canonical form, has been derived for the subclass of the DPH distributions characterised by an acyclic transit...
متن کاملAcyclic discrete phase type distributions: properties and a parameter estimation algorithm
This paper provides a detailed study on discrete phase type (DPH) distributions and its acyclic subclass referred to as acyclic-DPH (ADPH). Previously not considered similarities and differences between DPH and continuous phase type (CPH) distributions are investigated and minimal representations, called canonical forms, for the subclass of ADPH distributions are provided. We investigate the co...
متن کاملCanonical representation of discrete phase type distributions of order 2 and 3
In spite of the fact that discrete phase type (DPH) distributions are used almost as often as their continuous phase type (CPH) distributions canonical representations are not available for general (cyclic) DPH distributions. In this paper we investigate the canonical representation of DPH distributions of order 2 and 3. During the course of this investigation we nd DPH properties which essenti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016