Advanced calculus is necessary to prove rigorously the main properties of the Cauchy distribution. It is well known that the Cauchy distribution can be generated by a tangent transformation of the uniform distribution. By interpreting this transformation on a circle, it is possible to present elementary and intuitive proofs of some important and useful properties of the distribution.
@article{urn:eudml:doc:40380,
title = {Geometrical understanding of the Cauchy distribution.},
journal = {Q\"uestii\'o},
volume = {26},
year = {2002},
pages = {283-287},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40380}
}
Cuadras, Carles M. Geometrical understanding of the Cauchy distribution.. Qüestiió, Tome 26 (2002) pp. 283-287. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40380/