Non-parametric estimation for semi-Markov kernels with application to reliability analysis

Applied Stochastic Models and Data Analysis

Volumn 12, Issue 4, 1996, Pages 209-220

  Ouhbi, B ^a   Limnios, N ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Estimation of the transition function; Kaplan Meier estimator; Markov renewal process; Reliability

Indexed keywords

ESTIMATION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; RELIABILITY;

KAPLAN-MEIER ESTIMATOR; MARKOV RENEWAL PROCESS;

MARKOV PROCESSES;

EID: 0030387246     PISSN: 87550024     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-0747(199612)12:4<209::aid-asm284>3.0.co;2-t     Document Type: Article

References (8)

1. N. Limnios and G. Oprisan, 'How can apply semi-Markov processes', World Energy System J., Vol. 1, 1996.
2. H. Moore and R. Pyke, 'Estimation of the transition distribution of a Markov renewal process', Ann. Inst. Statist. Math., 20, 411-24 (1968).
3. S. W. Lagakos, C. J. Sommer and M. Zelen, 'Semi-Markov models for partially censored data', Biometrica, 65(2), 311-317 (1978).
4. P. Billingsley, Statistical Inference for Markov Process, University of Chicago, U.S.A., 1961.
5. E. L. Kaplan and P. Meier, 'Nonparametric estimation from incomplete observations', J. Am. Statist. Assoc., 53, 457-81 (1958).
6. R. Pyke and R. Schaufele, 'Limit theorems for Markov renewal process', Ann. Math. Statist., 35, 1746-1764 (1964).
7. A. Bousfiha, B. Delaporte and N. Limnios, 'Evaluation numérique de la fiabilité des systèmes semi-Markoviens', In Proc. FRANCORO, 11-14 June 1995. Mons, Belgium.
8. N. Limnios, 'Dependability analysis of semi-Markov systems', submitted for publication, 1995.