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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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File URL: http://cowles.yale.edu/sites/default/files/files/pub/d08/d0887.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 887.

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Length: 6 pages
Date of creation: 1989
Handle: RePEc:cwl:cwldpp:887
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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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