Title

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

Document Type

Discussion Paper

Publication Date

10-1-1988

CFDP Number

887

CFDP Pages

6

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 θ where θ is uniform on (–π/2, π/2) when X is standard Cauchy. A matrix generalization of this characterization theorem is also given.

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