Estimating the order of continuous phase-type distributions and Markov-modulated poisson processes

Communications in Statistics. Part C: Stochastic Models

Volumn 13, Issue 3, 1997, Pages 417-433

  Rydén, Tobias ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LUND UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141667843     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326349708807434     Document Type: Article

References (20)

1. Akaike, H. A new look at the statistical model identification. IEEE Trans. Auto. Control 19 (1974), 716-723.
2. Asmussen, S., Nerman, O., and Olsson, M. Fitting phase type distributions via the EM algorithm. To appear in Scand. J. Statist. (1996).
3. Baras, J. S. and Finesso, L. Consistent estimation of the order of hidden Markov chains. In Stochastic Theory and Adaptive Control, vol. 184 of Lecture Notes in Control and Informational Science. Springer-Verlag (1992), Berlin.
4. Bobbio, A. and Telek, M. A benchmark for PH estimation algorithms: Results for acyclic-PH. Stoch. Models 10 (1994), 661-677.
5. Çinlar, E. Introduction to Stochastic Processes. Prentice Hall (1975), Englewood Cliffs.
6. Chen, D. T. and Rieders, M. Cyclic Markov modulated Poisson processes in traffic characterization. Stoch. Models 12 (1996), 585-610.
7. Everitt, B. S. and Hand, D. J. Finite Mixture Distributions. Chapman and Hall (1981), London.
8. Freedman, D. Approximating Countable Markov Chains. Springer-Verlag (1983), New York.
9. Leroux, B. G. Consistent estimation of a mixing distribution. Ann. Statist. 20 (1992), 1350-1360.
10. Leroux, B. G. Maximum-likelihood estimation for hidden Markov models. Stoch. Proc. Appl. 40 (1992), 127-143.
11. McLachlan, G. J. On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Appl. Statist. 36 (1987), 318-324.
12. Meier-Hellstern, K. S. A fitting algorithm for Markov-modulated Poisson processes having two arrival rates. Eur. J. Oper. Res. 29 (1987), 370-377.
13. Neuts, M. F. Matrix-Geometric Solutions in Stochastic Models. Johns Hopkins University Press (1981), Baltimore.
14. Rydén, T. Parameter estimation for Markov modulated Poisson processes. Stoch. Models 10 (1994), 795-829.
15. Rydén, T. Consistent and asymptotically normal parameter estimates for Markov modulated Poisson processes. Scand. J. Stat. 22 (1995), 295-303.
16. Rydén, T. Estimating the order of hidden Markov models. Statistics 26 (1995), 345-354.
17. Rydén, T. On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions. J. Appl. Prob. 33 (1996), 640-653.
18. Schwarz, G. Estimating the dimension of a model. Ann. Statist. 6 (1978), 461-464.
19. Stoyan, D. Comparison Methods for Queues and Other Stochastic Models. Wiley (1983), Chichester.
20. Ziv, J. and Merhav, N. Estimating the number of states of a finite-state source. IEEE Trans. Inform. Theory 38 (1992), 61-65.