Advances in Probability Distributions with Given Marginals: Beyond the Copulas

ISBN-13: 9789401055345 / Angielski / Miękka / 2012 / 231 str.

G. Dall'aglio; S. Kotz; G. Salinetti

Opis

'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.

Recenzje

As the reader would most probably already conclude from the enthusiastic words in the first lines of this review, this book can be strongly recommended to probabilists and statisticians who deal with distributions with given marginals.
Mededelingen van het Wiskundig Genootschap

Spis treści

Fréenet Classes: the beginnings.- Thirty years of copulas.- Copulas and association.- Convolutions for dependent random variables.- Probabilistic interpretations of copulas and their convex sums.- A new approach to dependence in multivariate distributions.- A family of partial orderings for positive dependence among fixed marginal bivariate distributions.- Indecomposable marginal problems.- Fréchet-bounds and their applications.- Extremal solutions in the marginal problem.- On Eyraud-Farlie-Gumbel-Morgenstern random processes.- Author Index.