Probability and Statistical Models

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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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.

• Poisson process
• STATISTICA
• Weibull distributions
• change-point models
• exponential distribution
• gamma distributions
• lifetime distribution classes
• measure theory
• mixture models
• multivariate exponential extensions
• parametric life distributions
• probability models
• renewal theory
• shock models
• stochastic modeling
• quantitative finance

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)

• 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

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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