A typical copula is singular

On the singular components of a copula

We analyze copulas with a non-trivial singular component by using their Markov kernel representation. In particular, we provide existence results for copulas with a prescribed singular component. The constructions do not only help to deal with problems related to multivariate stochastic systems of lifetimes when joint defaults can occur with a non-zero probability, but even provide a copula max...

A note on the notion of singular copula

We clarify the link between the notion of singular copula and the concept of support of the measure induced by a copula.

Mutual information is copula entropy

In information theory, mutual information (MI) is a difference concept with entropy.[1] In this paper, we prove with copula [2] that they are essentially same – mutual information is also a kind of entropy, called copula entropy. Based on this insightful result, We propose a simple method for estimating mutual information. Copula is a theory on dependence and measurement of association.[2] Skla...

Squibs and Replies: Copula Omission Is a Grammatical Reflex

What Is Typical Language Development ?

In light of Musolino, Chunyo, and Landau’s recent findings and conclusions regarding syntax comprehension in Williams Syndrome (this issue), we first review the criteria used to determine whether the development of language is typical or atypical and, second, consider our current understanding of the causes of language delay. Given a certain set of theoretical assumptions (e.g., generative/modu...