確率と統計モデル：信頼性と金融数学における問題の基礎 Probability and Statistical Models : Foundations for Problems in Reliability and Financial Mathematics

Gupta, A. K./ Zeng, W./ Wu Y.

Birkhäuser（2010/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 267 p.
• 商品コード 9780817649869

基本説明

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.

Full Description

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.