Probability and Statistical Models

Foundations for Problems in Reliability and Financial Mathematics

  • Arjun K. Gupta
  • Wei-Bin Zeng
  • Yanhong Wu

Table of contents

  1. Front Matter
    Pages i-xii
  2. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 1-21
  3. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 23-43
  4. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 45-70
  5. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 71-86
  6. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 87-115
  7. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 117-140
  8. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 141-157
  9. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 159-178
  10. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 179-198
  11. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 199-219
  12. Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu
    Pages 221-235
  13. Back Matter
    Pages 237-267

About this book

Introduction

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. These models form the basis of well-known parametric lifetime distributions such as exponential, Weibull, and gamma distributions, as well as change-point and mixture models. The authors also consider more general notions of non-parametric lifetime distribution classes. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. Exercises and solutions to selected problems accompany each chapter in order to allow students to explore these foundations.

The key subjects covered include:

* Exponential distributions and the Poisson process

* Parametric lifetime distributions

* Non-parametric lifetime distribution classes

* Multivariate exponential extensions

* Association and dependence

* Renewal theory

* Problems in reliability, insurance, finance, and credit risk

This work differs from traditional probability textbooks in a number of ways. Since no measure theory knowledge is necessary to understand the material and coverage of the central limit theorem and normal theory related topics has been omitted, the work may be used as a single-semester senior undergraduate or first-year graduate textbook as well as in a second course on probability modeling. Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in their use of the book.

Probability and Statistical Models is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics.

Keywords

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

Authors and affiliations

  • Arjun K. Gupta
    • 1
  • Wei-Bin Zeng
    • 2
  • Yanhong Wu
    • 3
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  3. 3.Department of MathematicsCalifornia State University StanislausTurlockUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4987-6
  • Copyright Information Birkhäuser Boston 2010
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4986-9
  • Online ISBN 978-0-8176-4987-6
  • About this book