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Birkhäuser

Probability and Statistical Models

Foundations for Problems in Reliability and Financial Mathematics

  • Textbook
  • © 2010

Overview

Authors:
  1. Arjun K. Gupta

    1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Wei-Bin Zeng

    1. Department of Mathematics, University of Louisville, Louisville, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Yanhong Wu

    1. Department of Mathematics, California State University Stanislaus, Turlock, USA

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    You can also search for this author in PubMed   Google Scholar

  • Lays the foundation for solving problems in reliability, insurance, finance, and credit risk
  • Exercises and solutions to selected problems accompany each chapter
  • Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in the use of the book
  • Includes supplementary material: sn.pub/extras

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 1-21

  3. Exponential Distribution

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 23-43

  4. Poisson Process

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 45-70

  5. Parametric Families of Lifetime Distributions

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 71-86

  6. Lifetime Distribution Classes

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 87-115

  7. Multivariate Lifetime Distributions

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 117-140

  8. Association and Dependence

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 141-157

  9. Renewal Theory

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 159-178

  10. Risk Theory

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 179-198

  11. Asset Pricing Theory

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 199-219

  12. Credit Risk Modeling

    • Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 221-235

  13. Back Matter

    Pages 237-267
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Keywords

About this book

Probability models are now a vital componentof every scienti c investigation. This book is intended to introduce basic ideas in stochastic modeling, with emphasis on models and techniques. These models lead to well-known parametric lifetime distributions, such as exponential, Weibull, and gamma distributions, as well as the change-point and mixture models. They also motivate us to consider more general notions of nonparametric lifetime distribution classes. Particular attention has been paid to their applications in reliability, insurance mathematics, and economics. The following topics are the focus in this volume: 1. Exponential Distributions and the Poisson Process; 2. Parametric Lifetime Distributions; 3. Nonparametric Lifetime Distribution Classes; 4. Multivariate Exponential Extensions; 5. Association and Dependence; 6. Renewal Theory; 7. Applications to Reliability, Insurance, Finance, and Credit Risk. Chapter1providesnotationandbasicresultsinprobabilitytheorythatareneeded in the consequent chapters. Chapters 2 and 3 are devoted to models related to exponential distribution and Poisson processes. Particular attentions is paid to the characterizations of exponential distribution and the Poisson process. Two of the most important properties that characterize exponential distribution: the lack of memory property and constant failure rate are discussed in detail. Then the g- eralizations of exponential distribution are examined in three directions: through its parametric form that leads to parametric families of lifetime distributions; via notionsof aging(such as monotonefailure rate) that lead to a varietyof lifetime d- tribution classes; and through lifetime distributions of multiple component systems that lead to multivariate (mainly bivariate) exponential extension.

Reviews

From the reviews:

“This is a nice introductory textbook on stochastic processes, basically devoted to the Poisson process and its variants. The basic results are well illustrated by many examples with many problems at the end of each chapter. … The book is suitable for students that do not have an advanced training in the measure-theoretic aspects of probability or stochastic integration.” (Henryk Gzyl, Zentralblatt MATH, Vol. 1215, 2011)

Authors and Affiliations

  • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA

    Arjun K. Gupta

  • Department of Mathematics, University of Louisville, Louisville, USA

    Wei-Bin Zeng

  • Department of Mathematics, California State University Stanislaus, Turlock, USA

    Yanhong Wu

About the authors

Arjun K. Gupta is the author of a previous Birkhäuser book: Gupta/Chen, "Parametric Statistical Change Point Analysis," (978-0-8176-4169-6, 2000, 184 p.)  

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