A characterization of the Cauchy type
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- by Frank B. Knight PDF
- Proc. Amer. Math. Soc. 55 (1976), 130-135 Request permission
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 $ad - bc \ne 0$.References
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- F. B. Knight and P. A. Meyer, Une caractérisation de la loi de Cauchy, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 34 (1976), no. 2, 129–134. MR 397831, DOI 10.1007/BF00535680
- E. J. G. Pitman and E. J. Williams, Cauchy-distributed functions of Cauchy variates, Ann. Math. Statist. 38 (1967), 916–918. MR 210166, DOI 10.1214/aoms/1177698885
- H. L. Royden, Real analysis, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1963. MR 0151555
- E. J. Williams, Cauchy-distributed functions and a characterization of the Cauchy distribution, Ann. Math. Statist. 40 (1969), 1083–1085. MR 243657, DOI 10.1214/aoms/1177697613
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 130-135
- DOI: https://doi.org/10.1090/S0002-9939-1976-0394803-6
- MathSciNet review: 0394803