Probability and Statistical ModelsFoundations for Problems in Reliability and Financial Mathematics

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

1st Edition., 2011, XII, 267 p., Hardcover
ISBN: 978-0-8176-4986-9

A Birkhäuser Boston book

• 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

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.



Content Level » Upper undergraduate
Keywords » Poisson process - Weibull distributions - asset pricing theory - change-point models - credit risk modeling - exponential distribution - gamma distributions - lifetime distribution classes - mixture models - multivariate exponential extensions - parametric life distributions - probability models - renewal theory - risk theory - shock models - stochastic modeling


Related subjects » Applied Probability and Statistics - Engineering - Mathematics
Table of contents
Preface.- Preliminaries.- Exponential Distribution.- Poisson Process.- Parametric Families.- Lifetime Distribution Classes.- Multivariate Lifetime Distributions.- Association and Dependence.- Renewal Theory.- Risk Theory.- Asset Pricing Theory.- Credit Risk Modeling.- Bibliographical Notes.- Bibliography.- Answers and Solutions to Selected Problems.- Index.