Weibull Distribution Function
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If Mn is the mimimum of a sample of size n from the beta
distribution, Be(α,1), then the distribution of
n1/αMn
converges to the Weibull(α,1) distribution with scale parameter 1.
The Weibull(α,1) distribution has density
f(x) = α exp{-xα} xα-1 for x > 0
and distribution function,
F(x,α,1) = 1 - exp{-xα} for x > 0.
For example, F(1,1,1) = 1 - 1/e = .63212