| Description |
1 online resource |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Woodhead publishing in mechanical engineering ; number 720 |
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Woodhead Publishing in mechanical engineering ; no. 720.
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| Note |
Online resource; title from PDF title page (EBSCO, viewed November 25, 2015) |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Front Cover; Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach; Copyright; Dedication; Contents; Preface; Foreword; Biography of the external contributors to this book; Abbreviations; Chapter 1: Introduction to rare event probability estimation; 1.1 The book purposes; 1.2 What are the events of interest considered in this book?; 1.3 The book organization; References; Part One: Essential Background in Mathematics and System Analysis; Chapter 2: Basics of probability and statistics; 2.1 Probability theory operators; 2.1.1 Elements of vocabulary |
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2.1.2 Notion of dependence of random events andconditional probabilities 2.1.3 Continuous random variables; 2.1.3.1 Definitions; 2.1.3.2 Parameters of continuous random variables; 2.1.4 Continuous multivariate random variables; 2.1.4.1 Definitions and theorems; 2.1.4.2 Dependence of multivariate random variables ; 2.1.5 Point estimation ; 2.2 Random variable modeling; 2.2.1 Overview of common probability distributions; 2.2.1.1 Univariate distributions; Uniform distribution; Exponential distribution; Gaussian distribution; Truncated Gaussian distribution; Log-normal distribution |
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Cauchy distributionChi-squared distribution; Gamma and beta distributions; Laplace distribution; Some properties of univariate distributions; 2.2.1.2 Multivariate distributions; Multivariate normal distribution; 2.2.2 Kernel-based laws; 2.3 Convergence theorems and sampling algorithms; 2.3.1 Strong law of large numbers ; 2.3.2 Central limit theorem ; 2.3.3 Simulation of complex laws using the Metropolis-Hastings algorithm; 2.3.3.1 Markov chain; 2.3.3.2 Some properties of transition kernels; 2.3.3.3 The Metropolis-Hastings algorithm ; 2.3.3.4 Transformation of random variables; References |
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Chapter 3: The formalism of rare event probability estimation in complex systems3.1 Input-output system; 3.1.1 Description; 3.1.2 Formalism; 3.2 Time-variant system; 3.2.1 Description; 3.2.2 Formalism; 3.3 Characterization of a probability estimation; References; Part Two: Practical Overview of the Main Rare Event EstimationTechniques; Chapter 4: Introduction; 4.1 Categories of estimation methods; 4.2 General notations; 4.3 Description of the toy cases; 4.3.1 Identity function; 4.3.2 Polynomial square root function; 4.3.3 Four-branch system; 4.3.4 Polynomial product function; References |
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Chapter 5: Simulation techniques5.1 Crude Monte Carlo; 5.1.1 Principle; 5.1.2 Application on a toy case; Four-branch system; 5.1.3 Conclusion; 5.2 Simple variance reduction techniques; 5.2.1 Quasi-Monte Carlo; 5.2.2 Conditional Monte Carlo; 5.2.2.1 Principle; 5.2.2.2 Conclusion; 5.2.3 Control variates; 5.2.3.1 Principle; 5.2.3.2 Application on a toy case; Four-branch system; 5.2.3.3 Conclusion; 5.2.4 Antithetic variates; 5.2.4.1 Principle; 5.2.4.2 Application to a toy case; Identity function; 5.2.4.3 Conclusion; 5.3 Importance sampling; 5.3.1 Principle of importance sampling |
| Summary |
Comprehensive and insightful, this valuable resource offers a broad up-to-date view of techniques to estimate rare event probabilities, described with a unified notation to ease implementation plus a spectrum of simulation results on academic and realistic use cases. -- Edited summary from book. |
| Subject |
Engineering -- Statistical methods.
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Engineering mathematics.
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Aerospace engineering.
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Reliability (Engineering)
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Ingénierie -- Méthodes statistiques.
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Mathématiques de l'ingénieur.
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Aérospatiale (Ingénierie)
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Fiabilité.
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aerospace engineering.
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aeronautical engineering.
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MATHEMATICS -- Applied.
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MATHEMATICS -- Probability & Statistics -- General.
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Aerospace engineering
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Engineering mathematics
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Engineering -- Statistical methods
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Reliability (Engineering)
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Probabilitats.
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Enginyeria industrial -- Mètodes estadístics.
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| Added Author |
Balesdent, Mathieu, 1985- author.
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| Other Form: |
Original 9780081000915 008100091X (OCoLC)907204598 |
| ISBN |
9780081001110 (electronic bk.) |
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0081001118 (electronic bk.) |
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9780081000915 |
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008100091X |
| Standard No. |
AU@ 000057005866 |
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CHBIS 010796117 |
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CHNEW 001013241 |
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CHVBK 403941946 |
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DEBSZ 482377070 |
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GBVCP 856733059 |
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NLGGC 401010392 |
