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What family of distributions does the following cdf belong to? I know this is a dumb question but I've searched for quite a while online coming up empty.

$F(x) = \begin{cases} e^{-x^{-\alpha}} & x > 0 \\ 0 & x \leq 0 \end{cases} $

for $\alpha > 0$

qx123456
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1 Answers1

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This is a Fréchet distribution and is related to the Weibull distribution and the Gumbell distribution through the Fisher–Tippett–Gnedenko theorem. All are encountered in the context of extreme value theory.

Raskolnikov
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