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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of the Cauchy type


Author: Frank B. Knight
Journal: Proc. Amer. Math. Soc. 55 (1976), 130-135
DOI: https://doi.org/10.1090/S0002-9939-1976-0394803-6
MathSciNet review: 0394803
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Abstract | References | Additional Information

Abstract: It is proved that a random variable $ X$ is of Cauchy type if and only if $ (aX + b){(cX + d)^{ - 1}}$ has the same type as $ X$ for every $ a,b,c,d$ with $ ad - bc \ne 0$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0394803-6
Keywords: Cauchy distribution, type, projectivity, invariance, characterization
Article copyright: © Copyright 1976 American Mathematical Society