Flowgraph models for generalized phase type distributions having non-exponential waiting times

Scandinavian Journal of Statistics

Volumn 26, Issue 1, 1999, Pages 145-157

  Huzurbazar, Aparna V ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Markov process; Saddlepoint approximations; Semi Markov process; Survival analysis

Indexed keywords

EID: 0033240220     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00142     Document Type: Article

References (20)

1. Aalen, O. O. (1995). Phase type distributions in survival analysis. Scand. J. Statist. 22, 447-463.
2. Asmussen, S., Nerman, O. & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm. Scand. J. Statist. 23, 419-441.
3. Billard, L., Medley, G. & Anderson, R. (1990). The incubation period for the HIV virus. Lecture Notes in Biomath. 86, 21-35.
4. Butler, R. W. & Huzurbazar, A. V. (1997). Stochastic network models for survival analysis. J. Amer. Statist. Assoc. 92, 246-257.
5. Daniels, H. (1954). Saddlepoint approximations in statistics. Ann. Math. Statist. 25, 631-650.
6. DeGruttola, V. & Mayer, K. (1988). Assessing and modelling heterosexual spread of the human immunodeficiency virus in the United States. Rev. Infectious Diseases, 10, 138-150.
7. Dorf, R. (1989). Modern control systems, 5th edn. Addison-Wesley, London.
8. Harrison, P. G. (1990). Laplace transform inversion and passage-time distributions in Markov processes. J. Appl. Probab. 27, 74-87.
9. Huzurbazar, S. & Huzurbazar, A. (1999). Survival and hazard functions for progressive diseases using saddlepoint approximations. Biometrics, to appear.
10. Jensen, J. L. (1995). Saddlepoint approximations. Clarendon Press, New York.
11. Lagakos, S. (1976). A stochastic model for censored survival time in the presence of an auxiliary variable. Biometrics 32, 551-559.
12. Longini, I., Clark, W., Byers, R., Ward, J., Darrow, W., Lemp, G. & Hethcote, H. (1989). Statistical analysis of the stages of HIV infection using a Markov model. Statist. Med. 8, 831-843.
13. Mason, S. J. (1953). Feedback theory - some properties of signal flow graphs. Proc. Inst. Radio Engrs 41, 1144-1156.
14. Medley, G., Anderson, R. M., Cox, D. R. & Billard, L. (1987). Incubation period of AIDS in patients infected via blood transfusion. Nature 328, 719-721.
15. Olsson, M. (1996). Estimation of phase-type distributions from censored data. Scand. J. Statist. 23, 443-460.
16. Reid, N. (1988). Saddlepoint methods and statistical inference (with discussion). Statist. Sci. 3, 213-238.
17. Satten, G. A. & Longini, I. M. (1994). Estimation of incidence of HIV infection using cross-sectional marker surveys. Biometrics 50, 675-688.
18. Skovgaard, I. M. (1987). Saddlepoint expansions for conditional distributions. J. Appl. Probab. 24, 875-887.
19. Taylor, H. & Karlin, S. (1994). An introduction to stochastic modelling. Academic Press, Orlando.
20. Whitehouse, G. (1983). Flowgraph analysis. In Encyclopedia of statistical science, Vol. 3 (eds S. Kotz & N. Johnson). Wiley, New York.