I think the canonical Douglas Adams-ish phrase here would be "... without all that tedious mucking about with Bessel functions." Jim On Saturday, March 5, 2016, Eugene Salamin via math-fun < math-fun@mailman.xmission.com <javascript:_e(%7B%7D,'cvml','math-fun@mailman.xmission.com');>> wrote:
Here's a clever way to do it without having to muck with Bessel functions. Let x and y be independent Gaussian random variables with zero mean and unit variance. Then z = xy has the desired distribution.
Furthermore, the sum of n such products, has distribution
P[n](z) = (1 / (sqrt(pi) Gamma(n/2)) (|z| / 2)^((n-1)/2) BesselK[((n-1)/2] ( |z| ).
-- Gene
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