Polar distribution

In probability theory, the polar distribution is the probability distribution of angles occurring in a set of two-dimensional vectors, denoted by


 * $$p(\phi).\,$$

It is usually graphically represented as a closed curve


 * $$(x,y) = (r\cos\phi, \, r\sin\phi) $$,

where the radius $$r$$ equals the probability $$p$$.

Example
By computing the probability distribution of angles along a handwritten ink trace, a lobe-shaped polar distribution emerges. The main direction of the lobe in the first quadrant corresponds to the slant of handwriting (see: graphonomics).