Asymptotic Distribution of Centralized r When Sampling from Cauchy

12/27/2018

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by   Veson Lee, et al.

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Assume that X and Y are independent random variables, each having a Cauchy distribution with a known median. Taking a random independent sample of size n of each X and Y, one can then compute their centralized empirical correlation coefficient r. Analytically investigating the sampling distribution of this r appears possible only in the large n limit; this is what we have done in this article, deriving several new and interesting results.