Some new ratio-type copulas: theory and properties

In recent decades, the concept of copula has received a lot of attention. The fact that it can be used in so many branches of study is the main reason for its popularity. There are numerous copulas, which are sometimes classified as a family. In this paper, we highlight a novel type of ratio-type copula that has received little attention in the literature. We begin with a thorough examination of the simplest representative copula of this type, which can be expressed as $C (u, v)=uv (u+v)/ (1+uv)$. Relationships with known copulas, quadrant dependence, association properties and tail dependence properties are investigated. Then, we propose three parametric extensions of this new copula. Their basic features are discussed. Subsequently, a natural three-dimensional version is presented, and a higher-dimensional version is conjectured. The overall study is illustrated by several graphics and numerical tables.