An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research.

In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models.

Klappentext

Stochastic orders are a powerful tool for the comparison of probabilistic models in different areas as reliability, survival analysis, risks, finance and economics. Thebook provides a general background on this topic for students and researchers who want to use as a tool for their research. It provides detailed proofs of the main results and applications to several probabilistic models of interest in several fields.There aredetailed discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, and applications to probabilistic models.

Zusammenfassung

"Overall, this is a very welcome compact treatment of stochastic orders. Despite its introductory nature, the authors managed to include a wealth of useful results that are widely scattered across the literature." --Statistical Papers

"...a very elegant and concise introduction to stochastic orders. It covers all the elementary theory of the most widely used stochastic orders and, as such, has a broad range of applications in areas such as reliability, survival analysis, quantitative risk management, dependence modeling and economics." --Zentralblatt MATH

"...a comprehensive introduction to stochastic orders, and it is particularly suitable for students and researchers approaching this topic for the first time...The book is enriched with various examples and a large and updated bibliography on stochastic orders." --Mathematical Reviews

Inhalt
Chapter 1. Introduction1.1 Introduction and notation1.2 Parametric families of distributions1.3 Aging notions1.4 Dependence notionsChapter 2. Univariate stochastic orders2.1 Introduction2.2 Usual stochastic order2.3 Increasing convex order and related orders2.4 Comparison of residual lives2.5 Likelihood ratio order2.6 Dispersive orders2.7 Concentrations orders2.8 TTT orderChapter 3. Multivariate stochastic orders3.1 Introduction3.2 Multivariate stochastic order and related orders3.3 Multivariate increasing convex orders3.4 Comparison of multivariate residual lives3.5 Multivariate likelihood ratio order3.6 Multivariate dispersive order