In the present document, an extension of the statistical depth notion is introduced with
the aim to allow for measuring proximities between pairs of points. In particular, we
will extend the simplicial depth function, which measures how central is a point by
using random simplices (triangles in the two-dimensional space). The paper is
structured as follows: In first place, there is a brief introduction to statistical depth
functions. Next, the simplicial similarity function will be defined and its properties
studied. Finally, we will present a few graphical examples in order to show its behavior
with symmetric and asymmetric distributions, and apply the function to hierarchical
clustering
