Detecting positive quadrant dependence and positive function dependence

Positive Dependence of Signals

In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expecta...

Archimedean copulae and positive dependence

In this paper, we consider different issues related to Archimedean copulae and positive dependence. In the first part, we characterize Archimedean copulae that possess positive dependence properties such as multivariate total positivity of order 2 ðMTP2Þ and conditionally increasingness in sequence. In the second part, we investigate conditions for exchangeable binary sequences to admit an Arch...

Positive Dependence and Weak Convergence

A more general definition of MTP2 (multivariate total positivity of order 2) probability measure is given, without assuming the existence of a density. Under this definition the class of MTP2 measures is proved to be closed under weak convergence. Characterizations of the MTP2 property are proved under this more general definition. Then a precise definition of conditionally increasing measure i...

Positive Dependence Notions and Applications

Multivariate measures of positive dependence

The concept of dependency in a bivariate and in a multivariate setting has been largely studied in recent literature and the development of the theory of copulas has determined a great impact in the study of measures of dependence. This is of interest in economics, insurance, in finance and risk management and in many areas of applied probability and statistics. Several notions of positive depe...