Exponential Circular Distribution Motivated by Inverse Stereographic Projection

摘要

The stereographic projection that used in circular statistics is a mapping that projects a random variable from a circle onto a real line and the inverse stereographic projection is applicable to a distribution on the line for constructing a distribution on the circle. This paper proposed circular model such exponential on the real line to circle induced by inverse stereographic projection. We also evaluate the characteristics of the exponential circular model such as the mean resultant length, mean direction and circular variance.