Directional Statistics is a branch of Statistics that deals with data for which the unit circle, torus, cylinder, sphere, hypersphere, etc. are natural supports. Examples of circular variables include the direction of the wind at a wind farm, the time of the day of major Japanese earthquakes, or the start of the menstrual cycle represented on a 28 day body clock, while spherical variables typically occur in earth sciences (measurements on the surface of the earth) or astronomy (cosmic rays arrival directions). The unit torus is the natural support when two circular variables are jointly observed, and the cylinder when one circular variable and one linear variable are observed. So, joint observations of wind speed and direction are examples of so-called cylindrical data. Directional data arise in a wide variety of scientific disciplines including biology, medicine, astronomy, psychology, meteorology and geology.
The difficulty inherent to directional data compared to usual multivariate data lies in the fact that they take values on non-linear manifolds, rendering their analysis via standard multivariate methods impossible. This challenge, combined with the numerous domains of applications, is the driving force behind research in directional statistics.