Stochastic orders in reliability and risk : in honor of Professor Moshe Shaked
 Responsibility
 Haijun Li, Xiaohu Li, editors.
 Language
 English.
 Imprint
 New York : Springer, c2013.
 Physical description
 xxxi, 442 p. : ill. ; 25 cm.
 Series

Lecture notes in statistics (SpringerVerlag) 208.
Lecture notes in statistics (SpringerVerlag). Proceedings.
Access
Creators/Contributors
 Contributor
 Shaked, Moshe, 1945
 Li, Haijun.
 Li, Xiaohu.
Contents/Summary
 Bibliography
 Includes bibliographical references and indexes.
 Contents

 Theory of stochastic orders
 A global dependence stochastic order based on the presence of noise / Moshe Shaked, Miguel A. Sordo, and Alfonso SuárezLlorens
 Introduction
 Two previous ideas
 Two new ideas
 Some properties of the new orders
 The order <GDO3cx The order <GDO4st
 An application in reliability theory
 Duality theory and transfers for stochastic order relations / Alfred Müller
 Introduction
 Transfers and integral stochastic orders
 Duality theory
 Main results
 Examples
 Reversing conditional orderings / Rachele Foschi and Fabio Spizzichino
 Introduction
 The role of usual stochastic ordering in conditioning
 Remarkable properties of conditional orderings and related inversions
 Conditional orderings and dependence
 Applications of theorem 3.3.2
 Default contagion and dynamic dependence properties
 Conditional independence and reversed markov processes
 Discussion and conclusions
 Appendix
 Stochastic comparison of order statistics
 Multivariate comparisons of ordered data / Félix Belzunce
 Introduction
 Multivariate orders
 Multivariate models with ordered components
 Multivariate comparisons of ordered data
 Some additional comments
 Sample spacings with applications in multipleoutlier models / Nuria Torrado and Rosa E. Lillo
 Introduction
 Distributional properties of spacings
 Stochastic orderings of spacings from one sample
 Stochastic orderings of spacings from two samples
 Stochastic orderings of spacings from multipleoutlier models
 Conclusions
 Sample range of two heterogeneous exponential variables / Peng Zhao and Xiaohu Li
 Introduction
 Likelihood ratio ordering
 Hazard rate and dispersive orderings
 Stochastic orders in reliability
 On bivariate signatures for systems with independent modules / Gaofeng Da and Taizhong Hu
 Introduction
 Bivariate signatures
 Useful method to compute bivariate signatures
 The signatures of systems with independent modules
 Generalized series and parallel systems
 Redundancy systems
 An important class of 3state systems
 Some examples
 Stochastic comparisons of cumulative entropies / Antonio Di Crescenzo and Maria Longobardi
 Introduction
 Cumulative entropy
 Connections to reliability theory
 Inequalities and stochastic comparisons
 Dynamic cumulative entropy
 Empirical cumulative entropy
 Decreasing percentile residual life: properties and estimation / Alba M. FrancoPereira, Jacobo de Uña, Rosa E. Lillo, and Moshe Shaked
 Introduction
 Definitions and basic properties
 Relationship with the percentile residual life orders
 Estimation
 Extension of the estimator to the censored case
 A real data example
 Discussion
 A review on convolutions of gamma random variables / BahaEldin Khaledi and Subhash Kochar
 Introduction
 Preliminaries
 Magnitude and dispersive orderings
 Star ordering
 Right spread order of linear combinations
 On used systems and systems with used components / Xiaohu Li, Franco Pellerey, and Yinping You
 Introduction
 Main results
 Sufficient conditions for positive aging properties
 On allocation of active redundancies to systems: a brief review / Xiaohu Li and Weiyong Ding
 Introduction and preliminaries
 Redundancy at component level versus that at system level
 Redundancies with matching spares
 Redundancies with nonmatching spares
 Allocation of active redundancies to a koutofn system
 The case with i.i.d. components and redundancies
 The case with i.i.d components and i.i.d. Redundancies
 The case with stochastically ordered components
 Other allocations of active redundancies
 One single redundancy
 Several redundancies
 System with two dependent components
 Stochastic orders in risk analysis
 Dynamic risk measures within discretetime risk models / Hélène Cossette and Etienne Marceau
 Introduction
 Discretetime risk model
 Definitions
 Dynamic vaR and TVaR
 Numerical computation of the dynamic vaR and TVaR
 Dynamic TVaR and increasing convex order
 Discretetime risk model with dependent lines of business
 Additional definitions
 Dynamic TVaR and supermodular order
 Discretetime risk model with random income
 Additional definitions
 Dynamic TVaR and concordance order
 Acknowledgements
 Excess wealth transform with applications / Subhash Kochar and Maochao Xu
 Introduction and motivation
 Properties of excess wealth transform and order
 Excess wealth plot
 Applications
 Extreme risk analysis
 Reliability theory
 Auction theory
 Actuarial science
 Remarks
 Applications
 Intermediate tail dependence: a review and some new results / Lei Hua and Harry Joe
 Introduction
 Tail order and intermediate tail dependence
 Extreme value copula
 Elliptical copula
 Archimedean copula
 Resilience or frailty models
 Scale mixture models
 Remark and future work
 Secondorder conditions of regular variation and dreestype inequalities / Tiantian Mao
 Introduction
 Connections between 2ERV and 2RV
 Inequalities of drees type
 Individual and moving ratio charts for weibull processes / Francis Pascual
 Introduction
 Outline
 Related work
 Model assumptions
 Normal individual and moving range charts
 Shewhart control limits
 Run length properties of the Y and MR charts
 Discussion
 Individual and moving ratio charts for Weibull distribution
 Average run length and unbiasedness
 Average run length
 ARL unbiasedness
 Numerical results
 Control limits for the combined X/R charts
 ARLunbiasedness of X/R charts
 Sample size requirements for phase I
 An application
 Conclusion
 Appendix
 ARL computation for the moving range chart
 X/R ARL computation by markov chains
 On a slow server problem / Vladimir Rykov
 Introduction and motivation
 Problem formulation
 Optimality equation
 Transformation of optimality equations
 Monotonicity of optimal policies
 Conclusion
 Dependence comparison of multivariate extremes via stochastic tail orders / Haijun Li
 Introduction
 Stochastic tail orders
 Tail orthant orders
 Bibliography
 Author index
 Subject index.
 Publisher's Summary
 Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference's talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.
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Subjects
Bibliographic information
 Publication date
 2013
 Series
 Lecture notes in statistics/Proceedings, 18697240 ; 208
 Note
 Festschrift.
 Available in another form
 9781461468929 (online)
 (GyWOH)har135015010
 ISBN
 9781461468912 (hd.bd.)
 1461468914
 9781461468929 (eBook)
 1461468922 (eBook)