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Markov processes --- Renewal theory

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This book is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. Another unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis. The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers. It can also serve as a text for a six month research-oriented course at a Master or PhD level. The prerequisites are a background in probability theory and finite state space Markov chains. Vlad Stefan Barbu is associate professor in statistics at the University of Rouen, France, Laboratory of Mathematics ‘Raphaël Salem.’ His research focuses basically on stochastic processes and associated statistical problems, with a particular interest in reliability and DNA analysis. He has published several papers in the field. Nikolaos Limnios is a professor in Applied Mathematics at the University of Technology of Compiègne. His research interest concerns stochastic processes and statistics with application to reliability. He is the co-author of the books: Semi-Markov Processes and Reliability (Birkhäuser, 2001 with G. Oprisan) and Stochastic Systems in Merging Phase Space (World Scientific, 2005, with V.S. Koroliuk).

Markov processes --- Reliability (Engineering) --- DNA --- Markov, Processus de --- Fiabilité --- Mathematical models --- Analysis --- Modèles mathématiques --- DNA --Analysis --Mathematical models. --- Markov processes. --- Reliability (Engineering) --Mathematical models. --- Evaluation Studies as Topic --- Probability --- Stochastic Processes --- Epidemiologic Research Design --- Investigative Techniques --- Nucleic Acids --- Statistics as Topic --- Mathematical Concepts --- Nucleic Acids, Nucleotides, and Nucleosides --- Epidemiologic Methods --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Health Care Evaluation Mechanisms --- Quality of Health Care --- Public Health --- Phenomena and Processes --- Chemicals and Drugs --- Environment and Public Health --- Health Care Quality, Access, and Evaluation --- Health Care --- Markov Chains --- Models, Theoretical --- Reproducibility of Results --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models. --- Fiabilité --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Deoxyribonucleic acid --- Desoxyribonucleic acid --- Thymonucleic acid --- TNA (Nucleic acid) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Mathematics. --- Bioinformatics. --- Operations research. --- Management science. --- Probabilities. --- Statistics. --- Quality control. --- Reliability. --- Industrial safety. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Quality Control, Reliability, Safety and Risk. --- Operations Research, Management Science. --- Stochastic processes --- Deoxyribose --- Nucleic acids --- Genes --- Distribution (Probability theory. --- Mathematical statistics. --- System safety. --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Systems engineering --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Data processing --- Prevention --- Statistics . --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Standardization --- Quality assurance --- Quality of products --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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Probabilités --- Manuels d'enseignement supérieur --- Problèmes et exercices

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This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models. The systems discussed in the book include stochastic additive functionals, dynamical systems, stochastic integral functionals, increment processes and impulsive processes. All these systems are switched by Markov and semi-Markov processes whose phase space is considered in asympt

Stochastic processes --- Mathematical optimization --- Processus stochastiques --- Optimisation mathématique --- Stochastic processes. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Random processes --- Probabilities

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Nonparametric statistics has probably become the leading methodology for researchers performing data analysis. It is nevertheless true that, whereas these methods have already proved highly effective in other applied areas of knowledge such as biostatistics or social sciences, nonparametric analyses in reliability currently form an interesting area of study that has not yet been fully explored. Applied Nonparametric Statistics in Reliability is focused on the use of modern statistical methods for the estimation of dependability measures of reliability systems that operate under different conditions. The scope of the book includes: smooth estimation of the reliability function and hazard rate of non-repairable systems; study of stochastic processes for modelling the time evolution of systems when imperfect repairs are performed; nonparametric analysis of discrete and continuous time semi-Markov processes; isotonic regression analysis of the structure function of a reliability system, and lifetime regression analysis. Besides the explanation of the mathematical background, several numerical computations or simulations are presented as illustrative examples. The corresponding computer-based methods have been implemented using R and MATLAB®. A concrete modelling scheme is chosen for each practical situation and, in consequence, a nonparametric inference procedure is conducted. Applied Nonparametric Statistics in Reliability will serve the practical needs of scientists (statisticians and engineers) working on applied reliability subjects.

Nonparametric statistics. --- Reliability (Engineering) -- Statistical methods. --- Nonparametric statistics --- Reliability (Engineering) --- Mechanical Engineering --- Engineering & Applied Sciences --- Chemical & Materials Engineering --- Mathematics --- Physical Sciences & Mathematics --- Technology - General --- Mathematical Statistics --- Materials Science --- Industrial & Management Engineering --- Statistical methods --- System safety. --- Safety, System --- Safety of systems --- Systems safety --- Distribution-free statistics --- Statistics, Distribution-free --- Statistics, Nonparametric --- Engineering. --- Statistics. --- Quality control. --- Reliability. --- Industrial safety. --- Quality Control, Reliability, Safety and Risk. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Accidents --- Industrial safety --- Systems engineering --- Mathematical statistics --- Prevention --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Statistics . --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Industrial engineering --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products