Advances in Probability Distributions with Given Marginals : Beyond the Copulas

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'Et moi - ... - si j'avait su comment en rcvenir. One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canistcr labelled 'discarded non sense'. The scries is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. Read more... Abstract: 'Et moi - ... - si j'avait su comment en rcvenir. One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canistcr labelled 'discarded non sense'. The scries is divergent; therefore we may be Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series Front Matter....Pages i-xviii Frechet Classes: The Beginnings....Pages 1-12 Thirty Years of Copulas....Pages 13-50 Copulas and Association....Pages 51-74 Convolutions for Dependent Random Variables....Pages 75-93 Probabilistic Interpretations of Copulas and Their Convex Sums....Pages 95-112 A New Approach to Dependence in Multivariate Distributions....Pages 113-127 A Family of Partial Orderings for Positive Dependence Among Fixed Marginal Bivariate Distributions.....Pages 129-138 Indecomposable Marginal Problems....Pages 139-149 FréChet-Bounds and Their Applications....Pages 151-187 Extremal Solutions in the Marginal Problem....Pages 189-206 On Eyraud-Farlie-Gumbel-Morgenstern Random Processes....Pages 207-222 Back Matter....Pages 223-231