By G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)
As the reader may most likely already finish from theenthusiastic phrases within the first strains of this evaluate, this publication can bestrongly instructed to probabilists and statisticians who deal withdistributions with given marginals.
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Extra resources for Advances in Probability Distributions with Given Marginals: Beyond the Copulas
1 is the key to a new approach to the theory of Markov processes and to a new technique for constructing them. In the conven- tional approach, a Markov process is specified by an initial distribution and a family of transition probabilities satisfying the ChapmanKolmogorov equations. 4). It is different in principle from the conventional approach, for holding the transition probabilities fixed and varying the initial distribution necessarily varies all the marginal distributions, whereas holding the copulas of the process fixed and varying the initial distribution does not affect any other marginal distribution.
4, 617-627. Kimeldorf, G. and Sampson, A. R. (1978) Monotone dependence, Ann. Statist. 6, 895-903. Kimeldorf, G. and Sampson, A. R. (1987) Positive dependence orderings, Ann. Inst. Statist. Math. 39, 113-128. Kimeldorf, G. and Sampson, A. R. (1989) A framework for positive dependence, Ann. Inst. Statist. Math. 41, 31-45. Kotz, S. and Johnson, N. L. (1977) Proprietes de dependance des distributions interees generalisees deux variables FarlieGumbel-Morgenstern, C. R. Acad. Sci. Paris 285A, 277-280.
We conclude this section by remarking that copulas are employed by W. Whitt in , by W. Stute in  and  and, more recently, by A. W. Marshall and I. 01kin in . 8. WHEN MARGINS ARE FIXED By now the reader should be aware of the fact that any paper bear- ing a title that contains a phrase such as "when the margins are fixed" is a paper involving copulas. More often than not (since copulas are not yet as well-known as they might be) this involvement is implicit. Consequently, there is generally something to be gained - insight at the very least - by bringing the role of copulas explicitly to the fore.
Advances in Probability Distributions with Given Marginals: Beyond the Copulas by G. Dall’aglio (auth.), G. Dall’Aglio, S. Kotz, G. Salinetti (eds.)