메뉴 건너뛰기




Volumn 22, Issue 3, 2006, Pages 383-409

PH-invariant polytopes and coxian representations of phase type distributions

Author keywords

Aggregated Markov chain; Coxian distribution; Jordan canonical form; Matrix analytic methods; PH distribution; Polytope

Indexed keywords

ALGORITHMS; GEOMETRY; INVARIANCE; POLYNOMIALS; PROBABILITY; VECTORS;

EID: 33747172804     PISSN: 15326349     EISSN: 15324214     Source Type: Journal    
DOI: 10.1080/15326340600820349     Document Type: Article
Times cited : (13)

References (33)
  • 4
    • 0030502888 scopus 로고    scopus 로고
    • Fitting phase-type distributions via the em algorithm
    • Asmussen, S.; Nerman, O.; Olsson, M. Fitting phase-type distributions via the EM algorithm. Scand. J. Statist. 1996, 23, 419-441.
    • (1996) Scand. J. Statist. , vol.23 , pp. 419-441
    • Asmussen, S.1    Nerman, O.2    Olsson, M.3
  • 5
    • 0001259206 scopus 로고
    • On he identifiability problem for functions of finite Markov chains
    • Blackwell, D.; Koopmans, L. On he identifiability problem for functions of finite Markov chains. Ann. Math. Statist. 1957, 28, 1011-1015.
    • (1957) Ann. Math. Statist. , vol.28 , pp. 1011-1015
    • Blackwell, D.1    Koopmans, L.2
  • 6
    • 0001304763 scopus 로고
    • Characterizations of generalized hyperexponential distribution functions
    • Botta, R.F.; Harris, C.M.; Marchal, W.G. Characterizations of generalized hyperexponential distribution functions. Stochastic Models 1987, 3, 115-148.
    • (1987) Stochastic Models , vol.3 , pp. 115-148
    • Botta, R.F.1    Harris, C.M.2    Marchal, W.G.3
  • 7
    • 33646463200 scopus 로고    scopus 로고
    • Chakravarthy, S.R.; Alfa, A.S., Eds. Marcel Dekker: New York
    • Chakravarthy, S.R.; Alfa, A.S., Eds. Matrix-Analytic Methods in Stochastic Models; Marcel Dekker: New York, 1996.
    • (1996) Matrix-analytic Methods in Stochastic Models
  • 8
    • 27944488496 scopus 로고    scopus 로고
    • Linear positive systems and phase-type representations
    • Commault, C. Linear positive systems and phase-type representations. Positive Systems, Proceedings 2003, 294, 281-288.
    • (2003) Positive Systems, Proceedings , vol.294 , pp. 281-288
    • Commault, C.1
  • 9
    • 0013434041 scopus 로고
    • On dual and minimal phase-type representations
    • Commault, C.; Chelma, J.P. On dual and minimal phase-type representations. Stochastic Models 1993, 9, 421-434.
    • (1993) Stochastic Models , vol.9 , pp. 421-434
    • Commault, C.1    Chelma, J.P.2
  • 10
    • 0030488207 scopus 로고    scopus 로고
    • An invariant of representations of phase-type distributions and some applications
    • Commault, C.; Chemla, J.P. An invariant of representations of phase-type distributions and some applications. Journal of Applied Probability 1996, 33, 368-381.
    • (1996) Journal of Applied Probability , vol.33 , pp. 368-381
    • Commault, C.1    Chemla, J.P.2
  • 11
    • 0037002978 scopus 로고    scopus 로고
    • A generic property of phase-type representations
    • Commault, C.; Mocanu, S. A generic property of phase-type representations. Journal of Applied Probability 2002, 39, 775-785.
    • (2002) Journal of Applied Probability , vol.39 , pp. 775-785
    • Commault, C.1    Mocanu, S.2
  • 12
    • 0142199339 scopus 로고    scopus 로고
    • Phase-type distributions and representations: Some results and open problems for system theory
    • Commault, C.; Mocanu, S. Phase-type distributions and representations: some results and open problems for system theory. International Journal of Control 2003, 76, 566-580.
    • (2003) International Journal of Control , vol.76 , pp. 566-580
    • Commault, C.1    Mocanu, S.2
  • 13
    • 84959609465 scopus 로고
    • The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
    • Cox, D.R. The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proc. Camb. Phil. Soc. 1955, 51, 433-441.
    • (1955) Proc. Camb. Phil. Soc. , vol.51 , pp. 433-441
    • Cox, D.R.1
  • 14
    • 0020419336 scopus 로고
    • On the canonical representation of Markov processes modeling failure time distributions
    • Cumani, A. On the canonical representation of Markov processes modeling failure time distributions. Microelectronics and Reliability 1982, 22, 583-602.
    • (1982) Microelectronics and Reliability , vol.22 , pp. 583-602
    • Cumani, A.1
  • 15
    • 0346209968 scopus 로고
    • A geometric interpretation of the relations between the exponential and the generalized Erlang distributions
    • Dehon, M.; Latouche, G. A geometric interpretation of the relations between the exponential and the generalized Erlang distributions. Advances in Applied Probability 1982, 14, 885-897.
    • (1982) Advances in Applied Probability , vol.14 , pp. 885-897
    • Dehon, M.1    Latouche, G.2
  • 17
    • 33646443365 scopus 로고    scopus 로고
    • Spectral polynomial algorithms for computing bi-diagonal representations for phase type distributions and matrix-exponential distributions
    • He, Q.-M.; Zhang, H. Spectral polynomial algorithms for computing bi-diagonal representations for phase type distributions and matrix-exponential distributions. Stochastic Models 22, 289-317.
    • Stochastic Models , vol.22 , pp. 289-317
    • He, Q.-M.1    Zhang, H.2
  • 19
    • 0026837871 scopus 로고
    • Identifiability of hidden Markov information sources and their minimum degrees of freedom
    • Ito, H.; Amari, S.I.; Kobayashi, K. Identifiability of hidden Markov information sources and their minimum degrees of freedom. IEEE Trans. Inf. Theory 1992, 38, 324-333.
    • (1992) IEEE Trans. Inf. Theory , vol.38 , pp. 324-333
    • Ito, H.1    Amari, S.I.2    Kobayashi, K.3
  • 24
    • 0013388302 scopus 로고    scopus 로고
    • Sparse representations of phase type distributions
    • Mocanu, S.; Commault, C. Sparse representations of phase type distributions. Stochastic Models 1999, 15, 759-778.
    • (1999) Stochastic Models , vol.15 , pp. 759-778
    • Mocanu, S.1    Commault, C.2
  • 25
    • 0002542412 scopus 로고
    • Probability distributions of phase type
    • University of Louvain
    • Neuts, M.F. Probability distributions of phase type. In Liber Amicorum Prof. Emeritus H. Florin; University of Louvain, 1975; pp. 173-206.
    • (1975) Liber Amicorum Prof. Emeritus H. Florin , pp. 173-206
    • Neuts, M.F.1
  • 27
    • 0013378869 scopus 로고
    • On non-uniqueness of representations of phase-type distributions
    • O'Cinneide, C.A. On non-uniqueness of representations of phase-type distributions. Stochastic Models 1989, 5, 247-259.
    • (1989) Stochastic Models , vol.5 , pp. 247-259
    • O'Cinneide, C.A.1
  • 28
    • 0001784286 scopus 로고
    • Characterization of phase-type distributions
    • O'Cinneide, C.A. Characterization of phase-type distributions. Stochastic Models 1990, 6, 1-57.
    • (1990) Stochastic Models , vol.6 , pp. 1-57
    • O'Cinneide, C.A.1
  • 29
    • 0001574911 scopus 로고
    • Phase-type distributions and invariant polytope
    • O'Cinneide, C.A. Phase-type distributions and invariant polytope. Advances in Applied Probability 1991, 23, 515-535.
    • (1991) Advances in Applied Probability , vol.23 , pp. 515-535
    • O'Cinneide, C.A.1
  • 30
    • 0013042769 scopus 로고
    • Triangular order of triangular phase-type distributions
    • O'Cinneide, C.A. Triangular order of triangular phase-type distributions. Stochastic Models 1993, 9, 507-529.
    • (1993) Stochastic Models , vol.9 , pp. 507-529
    • O'Cinneide, C.A.1
  • 31
    • 0000519232 scopus 로고    scopus 로고
    • Phase-type distributions: Open problems and a few properties
    • O'Cinneide, C.A. Phase-type distributions: open problems and a few properties. Stochastic Models 1999, 15, 731-757.
    • (1999) Stochastic Models , vol.15 , pp. 731-757
    • O'Cinneide, C.A.1
  • 32
    • 0004267646 scopus 로고
    • Princeton University Press: New Jersey
    • Rockafellar, R.T. Convex Analysis; Princeton University Press: New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 33
    • 0030519097 scopus 로고    scopus 로고
    • On identifiability and order of continuous-time aggregated markov chains, Markov-modulated Poisson processes, and phase-type distributions
    • Ryden, T. On identifiability and order of continuous-time aggregated markov chains, Markov-modulated Poisson processes, and phase-type distributions. Journal of Applied Probability 1996, 33, 640-653.
    • (1996) Journal of Applied Probability , vol.33 , pp. 640-653
    • Ryden, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.