An Introduction to Stochastic Orders

An Introduction to Stochastic Orders

1st Edition - September 21, 2015

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  • Authors: Felix Belzunce, Carolina Riquelme, Julio Mulero
  • Paperback ISBN: 9780128037683
  • eBook ISBN: 9780128038260

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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

Product details

  • No. of pages: 174
  • Language: English
  • Copyright: © Academic Press 2015
  • Published: September 21, 2015
  • Imprint: Academic Press
  • Paperback ISBN: 9780128037683
  • eBook ISBN: 9780128038260

About the Authors

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

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