Geodesic
A Family of Distributions with the same Ratio Property as Normal Distribution
Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 631-636

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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. 
Fox, Charles. A Family of Distributions with the same Ratio Property as Normal Distribution. Canadian mathematical bulletin, Tome 8 (1965) no. 5, pp. 631-636. doi: 10.4153/CMB-1965-046-3
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     title = {A {Family} of {Distributions} with the same {Ratio} {Property} as {Normal} {Distribution}},
     journal = {Canadian mathematical bulletin},
     pages = {631--636},
     year = {1965},
     volume = {8},
     number = {5},
     doi = {10.4153/CMB-1965-046-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-046-3/}
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