An introduction to stochastic orders / Félix Belzunce, Universidad de Murcia, Spain, Carolina Martínez-Riquelme, Universidad de Murcia, Spain, Julio Mulero Universidad de Alicante, Spain.

Format:

Book

Author/Creator:

Belzunce, Félix, author.

Martínez-Riquelme, Carolina, author.

Mulero, Julio, author.

Language:

English

Subjects (All):

Securities--Mathematical models.

Securities.

Transaction costs--Mathematical models.

Transaction costs.

Liquidity (Economics)--Mathematical models.

Liquidity (Economics).

Physical Description:

1 online resource (175 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam, [Netherlands] : Academic Press, 2016.

Language Note:

English

Summary:

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. Introduces stochastic orders and its notationDiscusses different orders of univariate stochastic ordersExplains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders

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.

Notes:

Description based upon print version of record

Includes bibliographical references.

Description based on online resource; title from PDF title page (ebrary, viewed January 5, 2016).

ISBN:

0-12-803826-8

0-12-803768-7

OCLC:

932329947