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Point Process Models with Applications to Safety and Reliability

  • Book
  • © 1988

Overview

Authors:
  1. W. A. Thompson

    1. University of Missouri, Columbia, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • W. A. Thompson Jr
    Pages 1-8

  3. Point processes

    • W. A. Thompson Jr
    Pages 9-20

  4. Homogeneous Poisson processes

    • W. A. Thompson Jr
    Pages 21-31

  5. Application of point processes to a theory of safety assessment

    • W. A. Thompson Jr
    Pages 32-46

  6. Renewal processes

    • W. A. Thompson Jr
    Pages 47-52

  7. Poisson processes

    • W. A. Thompson Jr
    Pages 53-67

  8. Superimposed processes

    • W. A. Thompson Jr
    Pages 68-71

  9. Markov point processes

    • W. A. Thompson Jr
    Pages 72-78

  10. Applications of Markov point Processes

    • W. A. Thompson Jr
    Pages 79-92

  11. The order statistics process

    • W. A. Thompson Jr
    Pages 93-99

  12. Competing risk theory

    • W. A. Thompson Jr
    Pages 100-111

  13. Back Matter

    Pages 113-146
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Keywords

About this book

In teaching an elementary course in stochastic processes it was noticed that many seemingly deep results in point processes are readily accessible by the device of representing them in terms of random gap lengths between points. The possibility of representing point processes in terms of sequences of random variables rather than probability measures makes them mathemati­ cally simpler than general stochastic processes. Point processes can be studied using only the tools of elementary probability, that is the joint distributions of finitely many random variables. Given the wide applicability of point process models and the difficulty of access by the measure-theoretic route, it was determined that the simpler representation is of sufficient expository im­ portance to deserve emphasis. The present book is the result: it is specialized and short and therefore is called a monograph. In its development the material has been taught to several classes with pleasing results. Students have apparently understood theorems which by other methods appear difficult and deep. A few of the results, particularly on reliability, safety assessment and clustering, are original applied research. An alternative title for this monograph might be 'Point processes: What they are and what they are good for.

Authors and Affiliations

  • University of Missouri, Columbia, USA

    W. A. Thompson

Bibliographic Information

  • Book Title: Point Process Models with Applications to Safety and Reliability

  • Authors: W. A. Thompson

  • DOI: https://doi.org/10.1007/978-1-4613-1067-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Chapman and Hall 1988

  • Softcover ISBN: 978-1-4612-8406-2Published: 08 October 2011

  • eBook ISBN: 978-1-4613-1067-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XII, 146

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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