I know in the case of the bivariate normal distribution Kendall's Tau is given by $$ \tau=\frac{2}{\pi}\arcsin({\rho}) $$ where $\rho$ is Pearson's correlation. Can someone given a derivation of this result or provide a reference?
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$\begingroup$ Its name is GREINER's Equality and can see its proof in papers.ssrn.com/sol3/papers.cfm?abstract_id=2830471. $\endgroup$– user275214Feb 29, 2020 at 14:22
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$\begingroup$ Check math.stackexchange.com/q/3058888/321264. Can also be answered using math.stackexchange.com/q/255368/321264. $\endgroup$– StubbornAtomMar 31 at 15:23
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It is proven as Theorem 3.1 in Fang, Fang, & Kotz, The Meta-elliptical Distributions with Given Marginals Journal of Multivariate Analysis, Elsevier, 2002, 82, 1–16 but that relies on Theorem 2.22 in [K. T. Fang, Kotz, and Ng, "Symmetric Multivariate and Related Distribution," Chapman & Hall, London, 1990.] (to which I do not have access).