Axial Data Analysis. Random Vector. Axial Data. Properties of Axial data.
Sometime the observations are not direction but axes, that is, the unit vector and – are indistinguishable, so that it is which is observed. In this context it is appropriate to consider probability density functions for onwhich are anitpodally symmetric (diametrically opposite <an antipodal point on a sphere>)
Maps to a Projection
Note: the density is rotationally symmetric about
Where the integration is with respect to the uniform distribution on