This is an introductory chapter where the notions of positive dependence, with a particular interest in association, will be introduced. A few useful alternative characterizations of association will be studied. Basic properties are proved showing that, although some vagueness in its definition, association is reach enough to be an interesting structure. We include examples and applications that are illustrative of the scope and usefulness of this dependence notion. Association is natively a dependence structure on random variables, so we will discuss its extension to some more abstract spaces, highlighting the connections with the order structure of the underlying space. The chapter is concluded with a reference to other types of positive dependence and their relations. A brief discussion on negative dependence notions concludes the chapter.
KeywordsOrder Relation Dependence Structure Nondecreasing Function Positive Dependence Nonincreasing Function
- 5.Barlow, R., Proschan, F.: Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart & Winston, New York (1975) Google Scholar