Ebook: Distributions with given Marginals and Moment Problems

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.

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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.
Content:
Front Matter....Pages i-x
Optimal Bounds on the Average of a Rounded off Observation in the Presence of a Single Moment Condition....Pages 1-13
The Complete Solution of a Rounding Problem Under Two Moment Conditions....Pages 15-20
Methods of Realization of Moment Problems with Entropy Maximization....Pages 21-26
Matrices of Higher Moments: Some Problems of Representation....Pages 27-33
The Method of Moments in Tomography and Quantum Mechanics....Pages 35-52
Moment Problems in Stochastic Geometry....Pages 53-58
Fr?chet Classes and Nonmonotone Dependence....Pages 59-71
Comonotonicity, Rank-Dependent Utilities and a Search Problem....Pages 73-79
A Stochastic Ordering Based on a Decomposition of Kendall’s Tau....Pages 81-86
Maximum Entropy Distributions with Prescribed Marginals and Normal Score Correlations....Pages 87-92
On Bivariate Distributions with Polya-Aeppli or L?ders-Delaporte Marginals....Pages 93-98
Boundary Distributions with Fixed Marginals....Pages 99-106
On Approximation of Copulas....Pages 107-116
Joint Distribution of Two Uniform Random Variables When the Sum and the Difference are Independent....Pages 117-120
Diagonal Copulas....Pages 121-128
Copulas Constructed from Diagonal Sections....Pages 129-136
Continuous Scaling on a Bivariate Copula....Pages 137-142
Representation of Markov Kernels by Random Mappings under Order Conditions....Pages 143-160
How to Construct a Two Dimensional Random Vector with a Given Conditional Structure....Pages 161-171
Strassen’s Theorem for Group-Valued Charges....Pages 173-178
The Lancaster’s Probabilities on R2 and Their Extreme Points....Pages 179-190
On Marginalization, Collapsibility and Precollapsibility....Pages 191-198
Moment Bounds for Stochastic Programs in Particular for Recourse Problems....Pages 199-204
Probabilistic Constrained Programming and Distributions with Given Marginals....Pages 205-210
On an ?-Solution of Minimax Problem in Stochastic Programming....Pages 211-216
Bounds for Stochastic Programs — Nonconvex Case....Pages 217-222
Artificial Intelligence, the Marginal Problem and Inconsistency....Pages 223-234
Inconsistent Marginal Problem on Finite Sets....Pages 235-242
Topics in the Duality Theory for Mass Transfer Problems....Pages 243-252
Generalising Monotonicity....Pages 253-259
On Optimal Multivariate Couplings....Pages 261-273
Optimal Couplings between Onedimensional Distributions....Pages 275-281
Duality Theorems for Assignments with upper Bounds....Pages 283-290
Bounding Moments of an Order Statistic When Each K-Tuple is Independent....Pages 291-304
Back Matter....Pages 305-309

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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.
Content:
Front Matter....Pages i-x
Optimal Bounds on the Average of a Rounded off Observation in the Presence of a Single Moment Condition....Pages 1-13
The Complete Solution of a Rounding Problem Under Two Moment Conditions....Pages 15-20
Methods of Realization of Moment Problems with Entropy Maximization....Pages 21-26
Matrices of Higher Moments: Some Problems of Representation....Pages 27-33
The Method of Moments in Tomography and Quantum Mechanics....Pages 35-52
Moment Problems in Stochastic Geometry....Pages 53-58
Fr?chet Classes and Nonmonotone Dependence....Pages 59-71
Comonotonicity, Rank-Dependent Utilities and a Search Problem....Pages 73-79
A Stochastic Ordering Based on a Decomposition of Kendall’s Tau....Pages 81-86
Maximum Entropy Distributions with Prescribed Marginals and Normal Score Correlations....Pages 87-92
On Bivariate Distributions with Polya-Aeppli or L?ders-Delaporte Marginals....Pages 93-98
Boundary Distributions with Fixed Marginals....Pages 99-106
On Approximation of Copulas....Pages 107-116
Joint Distribution of Two Uniform Random Variables When the Sum and the Difference are Independent....Pages 117-120
Diagonal Copulas....Pages 121-128
Copulas Constructed from Diagonal Sections....Pages 129-136
Continuous Scaling on a Bivariate Copula....Pages 137-142
Representation of Markov Kernels by Random Mappings under Order Conditions....Pages 143-160
How to Construct a Two Dimensional Random Vector with a Given Conditional Structure....Pages 161-171
Strassen’s Theorem for Group-Valued Charges....Pages 173-178
The Lancaster’s Probabilities on R2 and Their Extreme Points....Pages 179-190
On Marginalization, Collapsibility and Precollapsibility....Pages 191-198
Moment Bounds for Stochastic Programs in Particular for Recourse Problems....Pages 199-204
Probabilistic Constrained Programming and Distributions with Given Marginals....Pages 205-210
On an ?-Solution of Minimax Problem in Stochastic Programming....Pages 211-216
Bounds for Stochastic Programs — Nonconvex Case....Pages 217-222
Artificial Intelligence, the Marginal Problem and Inconsistency....Pages 223-234
Inconsistent Marginal Problem on Finite Sets....Pages 235-242
Topics in the Duality Theory for Mass Transfer Problems....Pages 243-252
Generalising Monotonicity....Pages 253-259
On Optimal Multivariate Couplings....Pages 261-273
Optimal Couplings between Onedimensional Distributions....Pages 275-281
Duality Theorems for Assignments with upper Bounds....Pages 283-290
Bounding Moments of an Order Statistic When Each K-Tuple is Independent....Pages 291-304
Back Matter....Pages 305-309
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