In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.
Keywords: expected cumulative operational time, semi-Markov process, non-parametric estimation
@article{RO_2007__41_4_399_0,
author = {Ouhbi, Brahim and Boudi, Ali and Tkiouat, Mohamed},
title = {The expected cumulative operational time for finite {semi-Markov} systems and estimation},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {399--410},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {4},
doi = {10.1051/ro:2007029},
mrnumber = {2361293},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro:2007029/}
}
TY - JOUR AU - Ouhbi, Brahim AU - Boudi, Ali AU - Tkiouat, Mohamed TI - The expected cumulative operational time for finite semi-Markov systems and estimation JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2007 SP - 399 EP - 410 VL - 41 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro:2007029/ DO - 10.1051/ro:2007029 LA - en ID - RO_2007__41_4_399_0 ER -
%0 Journal Article %A Ouhbi, Brahim %A Boudi, Ali %A Tkiouat, Mohamed %T The expected cumulative operational time for finite semi-Markov systems and estimation %J RAIRO - Operations Research - Recherche Opérationnelle %D 2007 %P 399-410 %V 41 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro:2007029/ %R 10.1051/ro:2007029 %G en %F RO_2007__41_4_399_0
Ouhbi, Brahim; Boudi, Ali; Tkiouat, Mohamed. The expected cumulative operational time for finite semi-Markov systems and estimation. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 4, pp. 399-410. doi: 10.1051/ro:2007029
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