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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On a class of distribution functions where the quotient follows the Cauchy law


Author: R. G. Laha
Journal: Trans. Amer. Math. Soc. 93 (1959), 205-215
MSC: Primary 60.00
MathSciNet review: 0117770
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  • [1] R. G. Laha, An example of a nonnormal distribution where the quotient follows the Cauchy law, Proc. Nat. Acad. Sci. U.S.A. 44 (1958), 222–223. MR 0093049 (19,1201j)
  • [2] R. G. Laha, On the laws of Cauchy and Gauss, Ann. Math. Statist. 30 (1959), 1165–1174. MR 0108844 (21 #7556)
  • [3] P. Lévy, L'arithmétique des lois de probabilité, J. Math. Pures Appl. vol. 17 (1938) pp. 17-39.
  • [4] Eugene Lukacs and Otto Szász, Certain Fourier transforms of distributions, Canadian J. Math. 3 (1951), 140–144. MR 0041271 (12,823b)
  • [5] Eugene Lukacs, Remarks concerning characteristic functions, Ann. Math. Statist. 28 (1957), 717–723. MR 0090914 (19,889h)
  • [6] D. A. Raikov, On the decomposition of Gauss and Poisson laws, Izv. Akad. Nauk. SSSR Ser. Mat. vol. 2 (1938) pp. 91-124 (in Russian).
  • [7] George P. Steck, A uniqueness property not enjoyed by the normal distribution, Ann. Math. Statist. 29 (1958), 604–606. MR 0098442 (20 #4901)
  • [8] E. C. Titchmarsh, The theory of functions, Oxford, 1939.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1959-0117770-3
PII: S 0002-9947(1959)0117770-3
Article copyright: © Copyright 1959 American Mathematical Society