Probability and Statistical Models: Foundations for Problems in Reliability and Financial Mathematics

ISBN-13: 9780817649869 / Angielski / Twarda / 2010 / 267 str.

Arjun K. Gupta

Opis

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.

Recenzje

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)

Spis treści

Preliminaries.- Exponential Distribution.- Poisson Process.- Parametric Families of Lifetime Distributions.- Lifetime Distribution Classes.- Multivariate Lifetime Distributions.- Association and Dependence.- Renewal Theory.- Risk Theory.- Asset Pricing Theory.- Credit Risk Modeling.

O autorze

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.)  

Blurb

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.