An Introduction to Stochastic Orders

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.

Chapter 1. Introduction
1.1 Introduction and notation
1.2 Parametric families of distributions
1.3 Aging notions
1.4 Dependence notions
Chapter 2. Univariate stochastic orders
2.1 Introduction
2.2 Usual stochastic order
2.3 Increasing convex order and related orders
2.4 Comparison of residual lives
2.5 Likelihood ratio order
2.6 Dispersive orders
2.7 Concentrations orders
2.8 TTT order
Chapter 3. Multivariate stochastic orders
3.1 Introduction
3.2 Multivariate stochastic order and related orders
3.3 Multivariate increasing convex orders
3.4 Comparison of multivariate residual lives
3.5 Multivariate likelihood ratio order
3.6 Multivariate dispersive order