An Introduction to Stochastic Orders - 1st Edition - ISBN: 9780128037683, 9780128038260

An Introduction to Stochastic Orders

1st Edition

Authors: Felix Belzunce Carolina Riquelme Julio Mulero
eBook ISBN: 9780128038260
Paperback ISBN: 9780128037683
Imprint: Academic Press
Published Date: 21st September 2015
Page Count: 174
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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 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.

Key Features

  • Introduces stochastic orders and its notation
  • Discusses different orders of univariate stochastic orders
  • Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders


Graduate students, PhD students and researchers in probability and statistics

Table of Contents

  • Dedication
  • List of figures
  • List of tables
  • Preface
  • Chapter 1: Preliminaries
    • Abstract
    • 1.1 Introduction
    • 1.2 Univariate distribution notions
    • 1.3 Multivariate distribution notions
    • 1.4 Summary
  • Chapter 2: Univariate stochastic orders
    • Abstract
    • 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
    • 2.10 Summary
  • Chapter 3: Multivariate stochastic orders
    • Abstract
    • 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
    • 3.8 Summary
  • Conclusion
  • Bibliography


No. of pages:
© Academic Press 2016
Academic Press
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About the Author

Felix Belzunce

Affiliations and Expertise

University of Murcia, Spain

Carolina Riquelme

Affiliations and Expertise

University of Murcia, Spain

Julio Mulero

Affiliations and Expertise

University of Alicante, Spain


"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

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