Distributions with given Marginals and Moment Problems

1. Front Matter

   Pages i-x

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2. Optimal Bounds on the Average of a Rounded off Observation in the Presence of a Single Moment Condition

   • George A. Anastassiou

   Pages 1-13

3. The Complete Solution of a Rounding Problem Under Two Moment Conditions

   • Tomasz Rychlik

   Pages 15-20

4. Methods of Realization of Moment Problems with Entropy Maximization

   • Valerie Girardin

   Pages 21-26

5. Matrices of Higher Moments: Some Problems of Representation

   • E. Käärik

   Pages 27-33

6. The Method of Moments in Tomography and Quantum Mechanics

   • L. B. Klebanov, S. T. Rachev

   Pages 35-52

7. Moment Problems in Stochastic Geometry

   • Viktor Beneš

   Pages 53-58

8. Fréchet Classes and Nonmonotone Dependence

   • Marco Scarsini, Moshe Shaked

   Pages 59-71

9. Comonotonicity, Rank-Dependent Utilities and a Search Problem

   • Alain Chateauneuf, Michèle Cohen, Isaac Meilijson

   Pages 73-79

10. A Stochastic Ordering Based on a Decomposition of Kendall’s Tau

    • P. Capéraà, A.-L. Fougères, C. Genest

    Pages 81-86

11. Maximum Entropy Distributions with Prescribed Marginals and Normal Score Correlations

    • Michiel J. W. Jansen

    Pages 87-92

12. On Bivariate Distributions with Polya-Aeppli or Lüders-Delaporte Marginals

    • Violetta E. Piperigou

    Pages 93-98

13. Boundary Distributions with Fixed Marginals

    • Ene-Margit Tiit, Hele-Liis Helemäe

    Pages 99-106

14. On Approximation of Copulas

    • X. Li, P. Mikusiński, H. Sherwood, M. D. Taylor

    Pages 107-116

15. Joint Distribution of Two Uniform Random Variables When the Sum and the Difference are Independent

    • Giorgio Dall’Aglio

    Pages 117-120

16. Diagonal Copulas

    • Roger B. Nelsen, Gregory A. Fredricks

    Pages 121-128

17. Copulas Constructed from Diagonal Sections

    • Gregory A. Fredricks, Roger B. Nelsen

    Pages 129-136

18. Continuous Scaling on a Bivariate Copula

    • C. M. Cuadras, J. Fortiana

    Pages 137-142

19. Representation of Markov Kernels by Random Mappings under Order Conditions

    • Hans G. Kellerer

    Pages 143-160

20. How to Construct a Two Dimensional Random Vector with a Given Conditional Structure

    • Josef Štěpán

    Pages 161-171

The last decade has seen a remarkable development of the "Marginal and Moment Problems" as a research area in Probability and Statistics. Its attractiveness stemmed from its lasting ability to provide a researcher with difficult theoretical problems that have direct consequences for appli­ cations outside of mathematics. The relevant research aims centered mainly along the following lines that very frequently met each other to provide sur­ prizing and useful results : -To construct a probability distribution (to prove its existence, at least) with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. -To study the geometrical and topological structure of the set of prob­ ability distributions generated by such a property 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. These research aims characterize also, though only very generally, the scientific program of the 1996 conference "Distributions with given marginals and moment problems" held at the beginning of September in Prague, Czech Republic, to perpetuate the tradition and achievements of the closely related 1990 Roma symposium "On Frechet Classes" 1 and 1993 Seattle" AMS Summer Conference on Marginal Problem".

• Markov kernel
• Measure
• Probability distribution
• Random variable
• Stent
• artificial intelligence
• intelligence
• optimization
• programming

• Department of Mathematics, Czech Technical University, Prague, Czech Republic

  Viktor Beneš

• Department of Statistics, Charles University, Prague, Czech Republic

  Josef Štěpán

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