Stochastic Orders And Decision Under Risk

CONTENTS PREFACE v ACKNOWLEDGMENTS vii CONTRIBUTORS viii LECTURES AND SPEAKERS AT THE WORKSHOP x Remarks on a Random Surface D. JB. Abraham and C. M. Newman 1 Stochastic Order and Martingale Dynamics in Multivariate Life Length Models: A Review E. Arjas and L Norros 7 Preservation and Attenuation of Inequality as Measured by the Lorenz Order B. C. Arnold 25 Lorenz Ordering of Order Statistics B. C. Arnold and J. A. Villasenor 38 Stochastic Orders and Their Application to a Unified Approach to Various Concepts of Dependence and Association R. Bergmann 48 Second Order Bonferroni-Type, Product-Type and Setwise Probability Inequalities H. W. Block, T. Costigan, and A. R. Sampson 74 Optimal Stopping of Life Testing: Use of Stochastic Orderings in the Case of Conditionally Exponential Lifetimes C. Costantini and F. Spizzichino 95 Multivariate Probability Inequalities: Convolution Theorems, Composition Theorems, and Concentration Inequalities M. L. Eaton and M. D. Penman Stochastic Orderings in Reliability ίί.-W. Gaede 104 123 Representation Theorems for Measures of Location and for Measures of Dispersion A. Giovagnoli and G. Regoli 141 Orderings of Risks and Their Actuarial Applications W.-Jί. Heilmann and K.-J. Schrδter 157 Applications of Likelihood Orderings in Economics 174 I. Jewitt Stochastic Orders in Welfare Economics M. Le Breton 190 Ordering Regression Models of Gaussian Processes H. Luschgy 207 Xlll Multivariate Stochastic Orderings and Generating Cones of Functions A. W. Marshall 231 Stochastic Ordering for Markov Processes on Partially Ordered Spaces with Applications to Queueing Networks W. A. Massey 248 Some Theory of Stochastic Dominance K. Mosler and M. Scarsini 261 Bounds for Distributions with Multivariate Marginals L. Rύschendorf 285 Repair Policies and Stochastic Order T. if. Savits 311 Regular, Sample Path and Strong Convexity: A Review M. Shaked and J. G. Shanthikumar 320 Stochastic Orders and Comparison of Experiments E. Torgersen 334 Expectation Inequalities from Convex Geometry R. A. Vitale 372 Concentration Indices and Concentration Curves S. Yitzhaki and I. Olkin 380 XIV List of Contributors D. B. Abraham, Department of Theoretical Chemistry, Oxford University, Oxford 0X1 3UB, England Elja Arjas, Department of Applied Mathematics and Statistics, University of Oulu, Linnanmaa, SF-90570 Oulu 57, Finland Barry C. Arnold, Department of Statistics, University of California, Riverside, CA 92521, USA Reinhard Bergmann, Kronenstrafie 18, D-7888 Rheinfelden, Germany Henry W. Block, Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA Cristina Costantini, Dipartimento di Matematica, Universita "La Sapienza", Piazzale Aldo Moro 5,1-00185 Roma, Italy Timothy Costigan, Department of Statistics, The Ohio State University, 1958 Neil Avenue, Columbus, OH 43120-1247, USA Morris Eaton, School of Statistics, University of Minnesota, Minneapolis, MN 55455, USA Karl-Walter Gaede, Institut fur Statistik und Unternehmensforschung, Technische Universitat Mϋnchen, Arcisstrafie 21, D-8000 Mύnchen, Germany Alessandra Giovagnoli, Dipartimento di Scienze Statistiche, Universita di Perugia, Via Pascoli, C.P. 1315/11-06100 Perugia, Italy Wolf-Rudiger Heilmann, Lehrstuhl fur Versicherungswissenschaften, Universitat Karlsruhe, Postfach 69 80, D-7500 Karlsruhe 1, Germany Ian Jewitt, Department of Economics, University of Bristol, 40 Berkeley Square,