An Optimal Algorithm for Computing the Spherical Depth of Points in the Plane

David Bremner, Rasoul Shahsavarifar

For a distribution function $F$ on ${\mathbb{R}}^d$ and a point $q\in {\mathbb{R}}^d$, the \emph{spherical depth} $\SphD(q;F)$ is defined to be the probability that a point $q$ is cont…