McCullagh's parametrization of the Cauchy distributions

In probability theory, the "standard" Cauchy distribution is the probability distribution whose probability density function (pdf) is f ( x ) = 1 π ( 1 + x 2 ) {\displaystyle f(x)={1 \over \pi (1+x^{2})}} for x real. This has median 0, and first and third quartiles respectively −1 and +1.

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