A New Proof of Knight's Theorem on the Cauchy Distribution
We offer a new and straightforward proof of F.B. Knight's  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.
|Date of creation:||1989|
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|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
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