distributions with fixed marginals and related topics || front matter

Front MatterSource: Lecture Notes-Monograph Series, Vol. 28, Distributions with Fixed Marginals andRelated Topics (1996), pp. i-xixPublished by: Institute of Mathematical StatisticsStable URL: http://www.jstor.org/stable/4355876 .

Accessed: 10/06/2014 17:51

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Institute of Mathematical Statistics is collaborating with JSTOR to digitize, preserve and extend access toLecture Notes-Monograph Series.

http://www.jstor.org

This content downloaded from 194.29.185.203 on Tue, 10 Jun 2014 17:51:35 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=ims

http://www.jstor.org/stable/4355876?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Institute of Mathematical Statistics

LECTURE NOTES - MONOGRAPH SERIES

Distributions with Fixed Marginals

and Related Topics

Ludger R?schendorf, Berthold Schweizer,

and Michael D. Taylor, Editors

Volume 28




LECTURE NOTES-MONOGRAPH SERIES

Volume 28

Distributions with Fixed Marginals

and Related Topics

Ludger R?schendorf, Berthold Schweizer

and Michael D. Taylor, Editors


Hay ward, California




Lecture Notes-Monograph Series

Editorial Board

Andrew A. Barbour, Joseph Newton, and David Ruppert (Editor)

The production of the IMS Lecture Notes-Monograph Series is

managed by the IMS Business Office: Miriam Gasko Donoho, IMS

Treasurer, and Barbara J. Lindeman, IMS Business Manager.

Library of Congress Catalog Card Number: 96-77773

International Standard Book Number 0-940600-40-4

Copyright ? 1996 Institute of Mathematical Statistics

All rights reserved

Printed in the United States of America



PARTICIPANTS

Barry C. Arnold

Michel L. Balinski

Viktor Benes

Henry W. Block

Hans Colonius

Carlos M. Cuadras

Juan A. Cuesta-Albertos

Giorgio Dall'Aglio Paul Deheuvels

Jiu Ding David Feldman

M. J. Frank

Ryszard Grzaslewicz

Harry Joe

Abram Kagan

Andrzej Kaminski

Hans G. Kellerer

J. H. B. Kemperman Michael Lavine

Gerard Letac

Vladimir L'vovich Levin

Haijun Li

Xin Li

Anthony A. J. Marley Albert W. Marshall

Piotr Mikusinski

Hari Mukerjee

Roger ?. ? eisen

Ingram Olkin

Elwood T. Olsen

Michael Perlman

Svetlozar T. Rachev

Doraiswamy Ramachandran

Yosef Rinott

Jose A. Rodriguez-Lallena

Ludger R?schendorf

Tomasz Rychlik

University of California, Riverside

?cole Polytechnique, Paris

Czech Technical University

University of Pittsburgh

University of Oldenberg Universit?t de Barcelona

Universidad de Cantabria

Universit? Degli Studi di Roma

Universit? de Paris

University of Southern Mississippi

University of New Hampshire Illinois Institute of Technology

Politechnica, Wroclaw

University of British Columbia

University of Maryland at College Park

Polish Academy of Sciences, Katowice

University of Munich

Rutgers University Duke University Universit? Paul Sabatier

Central Institute of Mathematical Economics

Academy of Sciences, Moscow

University of Arizona

University of Central Florida

McGill University


and Western Washington University


Wichita State University Lewis and Clark College Stanford University Illinois Institute of Technology

University of Washington

University of California, Santa Barbara

California State University at Sacramento

University of California, San Diego Universidad de Almer?a

University of Freiburg Polish Academy of Sciences, Sopot

xi



Marco Scarsini

Geza Schay Berthold Schweizer

Carlo Sempi Moshe Shaked

Kathleen Shannon

Howard Sherwood

Rae Michael Shortt

Abe Sklar

Robert M. Tardiff

Michael D. Taylor

Ene-Margit Tut

Richard A. Vitale

Alexander Wilce

Calvin Williams

Stan Williams

Universit? D'Annunzio

University of Massachsusetts at Boston

University of Massachusetts at Amherst

Universit? di Lecce


Salisbury State University


Wesleyan University Illinois Institute of Technology

Salisbury State University


University of Tartu

University of Connecticut

University of Pittsburgh at Johnstown

Clemson University Utah State University

Xll



U



r o w*v



Referees

Barry C. Arnold

Henry W. Block

Juan A. Cuesta-Albertos

Giorgio Dall'Aglio David Feldman

M. J. Frank

Christian Genest

Ryszard Grzaslewicz

Harry Joe

Abram Kagan Hans G. Kellerer

J. H. B. Kemperman Vladimir L'vovich Levin

Albert W. Marshall

Piotr Mikusinski

Roger B. Nelsen

Elwood T. Olsen

Svetlozar T. Rachev

Doraiswamy Ramachandran

Gian-Carlo Rota

Ludger R?schendorf

Allan R. Sampson Marco Scarsini

Berthold Schweizer

Carlo Sempi Moshe Shaked

Howard Sherwood

Rae Michael S h?rt t

Abe Sklar

Michael D. Taylor Richard A. Vitale

Alexander Wilce

University of California, Riverside

University of Pittsburgh Universidad de Cantabria

Universit? Degli Studi di Roma

University of New Hampshire Illinois Institute of Technology Universit? de Laval, Cit? Universitaire

Politechnica, Wroclaw


University of Maryland at College Park

University of Munich

Rutgers University Central Institute of Mathematical Economics

Academy of Sciences, Moscow


and Western Washington University


Lewis and Clark College Illinois Institute of Technology

Univeristy of California, Santa Barbara

California State University at Sacramento

Massachusetts Institute of Technology

University of Freiburg

University of Pittsburgh Universit? D'Annunzio

University of Massachustts at Amherst

Universit? di Lecce



Wesleyan University Illinois Institute of Technology


University of Connecticut

University of Pittsburgh at Johnstown

xm



CONTENTS

Editors's Preface ?

Foreword vii

Participants xi

Referees xiii

Conference Program xiv

Random Variables, Distribution Functions, and Copulas - A Personal Look Backward and Forward 1

A. S klar

Distributions with Logistic Marginals and/or Conditionals 15

Barry C. Arnold

How Should Data be Rounded? 33

Michel L. Balinski

Isotonic Regression on Permutations 45

H. W. Block, S. Qian, and A. R. Sampson

Nonsquare "Doubly Stochastic" Matrices 65

R. M. Caron, Xin Li, P. Mikusinski, H. Sherwood, and

M. D. Taylor

A Distribution with Given Marginals and Given Regression Curve 76

C M. Cuadras

Doubly Stochastic Measures: Three Vignettes 84

David Feldman

Discretization for Stochastic Differential Equations, Lp

Wasserstein Metrics, and Econometrical Models 97

Matthias Gelbrich and Svetlozar T. Rachev

Families of m-Variate Distributions with Given Margins and m(m

- l)/2 Bivariate Dependence Parameters 120

Harry Joe

Ambiguity in Bounded Moment Problems 142

Hans G. Keller er

Proximity of Probability Measures with Common Marginals in a Finite Number of Directions 162

L. B. Klebanov and S. T. Rachev

Duality for a Non-Topological Version of the Mass Transportation Problem 175

Vladimir L. Levin

In Quest of Birkhoff's Theorem in Higher Dimensions 187

Xin Li, P. Mikusinski, H. Sherwood, and M. D. Taylor

Bounds for the Distribution of a Multivariate Sum 198

Haijun Li, Marco Scarsini, and Moshe Shaked

xvin



Copulas, Marginals, and Joint Distributions 213 Albert W. Marshall

Nonparametric Measures of Multivariate Association 223

Roger B. Nelsen

Derivability of Some Operations on Distribution Functions 233

Roger B. Nelsen, Jos? Juan Quesada-Molina, Berthold

Schweizer, and Carlo Sempi

Copulas and Markov Operators 244 Elwood T. Olsen, William F. Darsow, and Bao Nguyen

The Marginal Problem in Arbitrary Product Spaces 260 D. Ramachandran

Developments in Fr?chet-Bounds 273

Ludger R?schendorf

Order Statistics of Variables with Given Marginal Distributions 297 Tomasz Rychlik

Copulae of Capacities on Product Spaces 307 Marco Scarsini

Products of Vector Measures 319 R. M. Shortt

Moment Decompositions of Measure Spaces 328

Josef St?pan and Viktor Benes

Mixtures of Multivariate Quasi-Extremal Distributions

Having Given Marginals 337

Ene-Margit Tiit

Parametrizing Doubly Stochastic Measures 358 Richard A. Vitale

XIX



distributions with fixed marginals and related topics || front matter

Documents