PH-Invariant Polytopes and Coxian Representations of Phase Type Distributions

DOI10.1080/15326340600820349zbMath1159.60340OpenAlexW1985049710MaRDI QIDQ5446499

Qi-Ming He, Han-Qin Zhang

Publication date: 6 March 2008

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/15326340600820349

zbMATH Keywords

Jordan canonical formCoxian distributionMatrix analytic methodsPH-distributionPolytopeAggregated Markov chain

Mathematics Subject Classification ID

Continuous-time Markov processes on discrete state spaces (60J27) Canonical forms, reductions, classification (15A21)

Related Items (10)

Nonidentifiability of the two-state BMAP ⋮ New results about weakly equivalent \(\mathrm{MAP}_2\) and \(\mathrm{MAP}_3\) processes ⋮ Phase-type models for competing risks, with emphasis on identifiability issues ⋮ Identifiability of the \(\mathrm{MAP}_2/\mathrm{G}/1\) queueing system ⋮ Finding upper-triangular representations for phase-type distributions with 3 distinct real poles ⋮ Fitting procedure for the two-state batch Markov modulated Poisson process ⋮ Nonidentifiability of the Two-State Markovian Arrival Process ⋮ On absorption times and Dirichlet eigenvalues ⋮ Spectral Polynomial Algorithms for Computing Bi-Diagonal Representations for Phase Type Distributions and Matrix-Exponential Distributions ⋮ Building mean field ODE models using the generalized linear chain trick & Markov chain theory

Cites Work

• Unnamed Item
• Unnamed Item
• Simultaneous equations models in applied search theory
• On dual and minimal phase-type representations
• Phase-type distributions and invariant polytopes
• Characterization of phase-type distributions
• On non-uniqueness of representations of phase-type distributions
• A geometric interpretation of the relations between the exponential and generalized Erlang distributions
• Identifiability of hidden Markov information sources and their minimum degrees of freedom
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Phase-type distributions: open problems and a few properties
• Sparse representations of phase-type distributions
• Triangular order of triangular phase-type distributions^∗
• Phase-type distributions and representations: Some results and open problems for system theory
• Applied Probability and Queues
• On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions
• Characterizations of generalized hyperexponential distribution functions
• A generic property of phase-type representations
• An invariant of representations of phase-type distributions and some applications
• Convex Analysis
• On the Identifiability Problem for Functions of Finite Markov Chains

This page was built for publication: PH-Invariant Polytopes and Coxian Representations of Phase Type Distributions