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A Family of Distributions with the same Ratio Property as Normal Distribution

Published online by Cambridge University Press:  20 November 2018

Charles Fox
Charles Fox*
Affiliation:
McGill University
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If U and V are independent random variables, both drawn from the Normal distribution, then it is known that the distribution of U/V follows the Cauchy law, i. e. has frequency function 1/π(1+x2). Conversely if U and V are independently drawn from the same distribution and U/V is known to follow the Cauchy law of distribution must U and V be necessarily drawn from a Normal distribution? This question has been considered by several authors ([3], [4], [5], [7]) who have obtained several examples to show that the ratio property above is not confined to the Normal distribution.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 631 - 636
Copyright
Copyright © Canadian Mathematical Society 1965

References

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