An X validated question on an efficient way to simulate the largest order statistics of a Rayleigh (large) sample. Named after the 1904 Nobel recipient, John Strutt. This is not a commonly used distribution in statistics, since it coincides with the χ2 distribution. Anyway, thanks to its compact, closed form cdf, the largest order statistics can be directly simulated, at a constant cost in the sample size, as
or equivalently as
since the smallest order statistic from a Uniform sample, U(1), is distributed from a Be(1,N) distribution.
