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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,