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Distributions with Given Marginals and Moment Problems - Viktor Benes

Distributions with Given Marginals and Moment Problems

By: Viktor Benes (Editor), Josef Stepan (Editor)

Hardcover Published: January 2010
ISBN: 9780792345732
Number Of Pages: 309

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This volume contains the Proceedings of the 1996 Prague Conference on 'Distributions with Given Marginals and Moment Problems'. It provides researchers with difficult theoretical problems that have direct consequences for applications outside mathematics. Contributions centre around the following two main themes. Firstly, an attempt is made to construct a probability distribution, or at least prove its existence, with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. Secondly, the geometrical and topological structures of the set of probability distributions generated by such a property are studied, mostly with the aim to propose a procedure that would result in a stochastic model with some optimal properties within the set of probability distributions. Topics that are dealt with include moment problems and their applications, marginal problems and stochastic order, copulas, measure theoretic approach, applications in stochastic programming and artificial intelligence, and optimization in marginal problems. Audience: This book will be of interest to probability theorists and statisticians.

Preface
Acknowledgement
Optimal bounds on the average of a rounded off observation in the presence of a single moment conditionp. 1
The complete solution of a rounding problem under two moment conditionsp. 15
Methods of realization of moment problems with entropy maximizationp. 21
Matrices of higher moments: some problems of representationp. 27
The method of moments in tomography and quantum mechanicsp. 35
Moment problems in stochastic geometryp. 53
Frehet classes and nonmonotone dependencep. 59
Comonotonicity, rank-dependent utilities and a search problemp. 73
A stochastic ordering based on a decomposition of Kendall's taup. 81
Maximum entropy distributions with prescribed marginals and normal score correlationsp. 87
On bivariate distributions with Polya-Aeppli or Luders-Delaporte marginalsp. 93
Boundary distributions with fixed marginalsp. 99
On approximations of copulasp. 107
Joint distributions of two uniform random variables when the sum and differences are independentp. 117
Diagonal copulasp. 121
Copulas constructed from diagonal sectionsp. 129
Continuous scaling on a bivariate copulap. 137
Representation of Markov kernels by random mappings under order conditionsp. 143
How to construct a two dimensional random vector with a given conditional structurep. 161
Strassen's theorem for group-valued chargesp. 173
The Lancaster's probabilities on R[subscript 2] and their extreme pointsp. 179
On marginalization, collapsibility and precollapsibilityp. 191
Moment bounds for stochastic programs in particular for recourse problemsp. 199
Probabilistic constrained programming and distributions with given marginalsp. 205
On an [epsilon]-solution of minimax problem in stochastic programmingp. 211
Bounds for stochastic programs - nonconvex casep. 217
Artificial intelligence, the marginal problem and inconsistencyp. 223
Inconsistent marginal problem on finite setsp. 235
Topics in the duality for mass transfer problemsp. 243
Generalising monotonicityp. 253
On optimal multivariate couplingsp. 261
Optimal couplings between one-dimensional distributionsp. 275
Duality theorems for assignments with upper boundsp. 283
Bounding the moments of an order statistics if each k-tuple is independentp. 291
Subject Indexp. 305
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345732
ISBN-10: 0792345738
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 309
Published: January 2010
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.63