Matching moments for acyclic discrete and continuous phase-type distributions of second order

M. Telek, A. Heindl

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

The problem of matching moments to phase-type (PH) distributions occurs in many applications. Often, low dimensions of the selected distributions are desired in order to meet state space constraints. It is obvious that the three parameters of acyclic PH distributions of second order - be they continuous (ACPH(2)) or discrete (ADPH(2)) - can be fitted to three given moments provided that these are feasible. For both types of PH distributions, this paper provides the permissible ranges by giving the immanent lower and upper (if existing) bounds for the first three moments. For moments which obey these bounds an exact and minimal (with respect to the dimension of the representation) analytic mapping of three moments into ACPH(2) or ADPH(2) distributions is presented. Besides the unified treatment of the discrete and continuous cases, the contribution of this paper mainly consists in the presentation of exhaustive analytic third-moment bounds, which allow to go beyond existing low-order moment-fitting techniques - with respect to either the range of applicability or the precision or the order of the resulting PH distributions.

Original languageEnglish
Pages (from-to)47-56
Number of pages10
JournalInternational Journal of Simulation: Systems, Science and Technology
Volume3
Issue number3-4
Publication statusPublished - Dec 1 2002

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Moment Matching
Phase-type Distribution
Continuous Distributions
Moment
Range of data
State Space

Keywords

  • Discrete and continuous
  • Moment bounds
  • Moment fitting
  • PH-type distributions

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation

Cite this

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N2 - The problem of matching moments to phase-type (PH) distributions occurs in many applications. Often, low dimensions of the selected distributions are desired in order to meet state space constraints. It is obvious that the three parameters of acyclic PH distributions of second order - be they continuous (ACPH(2)) or discrete (ADPH(2)) - can be fitted to three given moments provided that these are feasible. For both types of PH distributions, this paper provides the permissible ranges by giving the immanent lower and upper (if existing) bounds for the first three moments. For moments which obey these bounds an exact and minimal (with respect to the dimension of the representation) analytic mapping of three moments into ACPH(2) or ADPH(2) distributions is presented. Besides the unified treatment of the discrete and continuous cases, the contribution of this paper mainly consists in the presentation of exhaustive analytic third-moment bounds, which allow to go beyond existing low-order moment-fitting techniques - with respect to either the range of applicability or the precision or the order of the resulting PH distributions.

AB - The problem of matching moments to phase-type (PH) distributions occurs in many applications. Often, low dimensions of the selected distributions are desired in order to meet state space constraints. It is obvious that the three parameters of acyclic PH distributions of second order - be they continuous (ACPH(2)) or discrete (ADPH(2)) - can be fitted to three given moments provided that these are feasible. For both types of PH distributions, this paper provides the permissible ranges by giving the immanent lower and upper (if existing) bounds for the first three moments. For moments which obey these bounds an exact and minimal (with respect to the dimension of the representation) analytic mapping of three moments into ACPH(2) or ADPH(2) distributions is presented. Besides the unified treatment of the discrete and continuous cases, the contribution of this paper mainly consists in the presentation of exhaustive analytic third-moment bounds, which allow to go beyond existing low-order moment-fitting techniques - with respect to either the range of applicability or the precision or the order of the resulting PH distributions.

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