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An introduction to stochastic orders. (English) Zbl 1366.60001

Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-803768-3/pbk). xv, 157 p. (2016).
This booklet is 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.
Definitions and discussions of fundamental properties of several univariate and multivariate stochastic orderings are given with applications to probabilistic models of interest.
The book is completed by a lot of illustrations and very useful comparison tables for most popular family of parametric distributions.
It might serve as a textbook for an introductory course on stochastic orders as well as a very useful handbook where the academic instructor or the more experienced researcher can find the relevant theory, specific references for further study and a comprehensive collections of proofs.

MSC:

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60E15 Inequalities; stochastic orderings
60G60 Random fields
60Kxx Special processes
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