Estimation of Kernel, Availability and Reliability of Semi-Markov Systems
Brahim Ouhbi, Nikolaos Limnios · Birkhäuser Boston eBooks · 1999
In this paper, we propose a new estimator for an absolutely continuous semi-Markov kernel based on its transition hazard rate estimator. We also give rigorous derivations of properties as strong consistency and weak convergence of this estimator. Estimators of Markov renewal matrix and semi-Markov transition matrix are also given as well as their asymptotic properties. From this estimator, we obtain estimators of reliability and availability and show that these ones are also strongly consistent.