A New Proof of Knight's Theorem on the Cauchy Distribution

We offer a new and straightforward proof of F.B. Knight's [3] theorem that the Cauchy type is characterized by the fact that it has no atom and is invariant under the involution i : x -> -1/x. Our approach uses the representation X = tan theta where theta is uniform on (-pi/2,pi/2) when X is standard Cauchy. A matrix generalization of this characterization theorem is also given.

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Year of publication:	1989
Authors:	Phillips, Peter C.B.
Institutions:	Cowles Foundation for Research in Economics, Yale University
Subject:	Cauchy distribution \| Involution \| Matrix variate \| Uniform distribution

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Extent:	application/pdf
Series:	Cowles Foundation Discussion Papers.
Type of publication:	Book / Working Paper
Language:	English
Notes:	The price is None Number 887 6 pages
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005762834