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An introduction to stochastic orders /

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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...

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Bibliographic Details
Main Authors: Belzunce, Félix (Author), Martínez-Riquelme, Carolina (Author), Mulero, Julio (Author)
Corporate Author: ScienceDirect (Online service)
Format: eBook
Language:English
Language Notes:English.
Published: Amsterdam, [Netherlands] : Academic Press, 2016.
Subjects:
Securities > Mathematical models.
Transaction costs > Mathematical models.
Liquidity (Economics) > Mathematical models.
Coûts de transaction > Modèles mathématiques.
Liquidité (Économie politique) > Modèles mathématiques.
Liquidity (Economics) > Mathematical models
Securities > Mathematical models
Transaction costs > Mathematical models
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Front Cover
  • An Introduction to Stochastic Orders
  • Copyright
  • Dedication
  • Contents
  • List of figures
  • List of Tables
  • Preface
  • Chapter 1: Preliminaries
  • 1.1 Introduction
  • 1.2 Univariate distribution notions
  • 1.2.1 The survival and the quantile function
  • 1.2.2 The stop-loss function
  • 1.2.3 The hazard rate and mean residual life functions
  • 1.2.4 Risk measures based on the quantile function
  • 1.2.5 Measures of concentration, inequality, and deprivation
  • 1.2.6 Total time on test transform
  • 1.2.7 Total positivity
  • 1.2.8 Parametric families of univariate distributions
  • 1.3 Multivariate distribution notions
  • 1.3.1 The standard construction
  • 1.3.2 Copulas
  • 1.3.3 The multivariate dynamic hazard rate and mean residual life functions
  • 1.3.4 Dependence notions
  • 1.3.5 Parametric families of multivariate distributions
  • 1.4 Summary
  • Chapter 2: Univariate stochastic orders
  • 2.1 Introduction
  • 2.2 The usual stochastic order
  • 2.3 The increasing convex order and related orders
  • 2.4 The hazard rate and mean residual life orders
  • 2.5 The likelihood ratio order
  • 2.6 Dispersive orders
  • 2.7 Concentration orders
  • 2.8 The total time on test transform order
  • 2.9 Applications
  • 2.9.1 Comparison of parametric families of distributions
  • 2.9.2 Comparison of coherent systems and distorted distributions
  • 2.9.3 Comparison of individual and collective risks and shock models
  • 2.10 Summary
  • Chapter 3: Multivariate stochastic orders
  • 3.1 Introduction
  • 3.2 The multivariate usual stochastic order
  • 3.3 Multivariate increasing convex orders
  • 3.4 Multivariate residual life orders
  • 3.5 The multivariate likelihood ratio order
  • 3.6 The multivariate dispersive order
  • 3.7 Applications
  • 3.7.1 Comparisons of mixtures of conditionally independent random vectors
  • 3.7.2 Comparisons of ordered data.
  • 3.8 Summary
  • Conclusion
  • Bibliography
  • Back Cover.