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

Peter Phillips

No 887, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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.

Keywords: Cauchy distribution; Involution; Matrix variate; Uniform distribution (search for similar items in EconPapers)
Pages: 6 pages
Date: 1989
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