SOME CHARACTERIZATIONS OF THE CAUCHY DISTRIBUTION |
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Authors: | B. C. Arnold |
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Affiliation: | Iowa State University |
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Abstract: | If X and Y are independent standard Cauchy random variables then (i) Y and (X+Y)/(1-Xu) are independent, (ii) X and (X + Y)/(1 -XU) are identically distributed, and (iii) X and 2X/(1-X2) are identically distributed. Each of these three properties is shown to characterize the Cauchy distribution among absolutely continuous distributions. Some related uniform characterizations are discussed. |
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