Geodesic
A Characterization of the Normal andWeibull Distributions
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 257-260

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Let X and Y be two independent normal variates each distributed with zero mean and a common variance. Then the quotient X/Y has the Cauchy distribution symmetrical about the origin. Of particular interest in recent years has been the converse problem and examples of non-normal distributions with a Cauchy distribution for the quotient have been illustrated by Mauldon [9], Laha [2; 3; 4] and Steck [10]. 
Seshadri, V. A Characterization of the Normal andWeibull Distributions. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 257-260. doi: 10.4153/CMB-1969-031-2
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[1] 1. Kawata, T. and Sakamoto, H., On the characterization of the normal distribution by the independence of the sample mean and the sample variance. J. Math. Soc. Japan 1 (1949) 111–115. Google Scholar

[2] 2. Laha, R. G., An example of a non-normal distribution where the quotient follows the Cauchy law. Proc. Nat. Acad. Sci. U.S.A. 44 (1958) 222–223. Google Scholar

[3] 3. Laha, R. G., On the laws of Cauchy and Gauss. Ann. Math. Stat. 30 (1959) 1165–1174. Google Scholar

[4] 4. Laha, R. G., On a class of distribution functions where the quotient follows the Cauchy law. Trans. Amer. Math. Soc. 93 (1959) 205–215. Google Scholar

[5] 5. Laha, R. G., Lukacs, E., and Newman, M., On the independence of a sample central moment and the sample mean. Ann. Math. Stat. 31 (1960) 1028–1033. Google Scholar

[6] 6. Lukacs, E., A characterization of the normal distribution. Ann. Math. Stat. 13 (1942) 91–93. Google Scholar

[7] 7. Lukacs, E., A characterization of the gamma distribution. Ann. Math. Stat. 26 (1955) 319–324. Google Scholar

[8] 8. Lukacs, E., The stochastic independence of symmetric and homogeneous linear and quadratic statistics. Ann. Math. Stat. 23 (1952) 442–449. Google Scholar

[9] 9. Mauldon, J. G., Characterizing properties of statistical distributions. Quart. J. Math. Oxford Ser. (2) 7 (1956) 155–160. Google Scholar

[10] 10. Steck, G. P., A uniqueness property not enjoyed by the normal distribution. Ann. Math. Stat. 31 (1958) 1028–1033. Google Scholar

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