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Fisher–Tippett–Gnedenko theorem
In
statistics
, the
Fisher–Tippett–Gnedenko theorem
(also the
Fisher–Tippett theorem
or the
extreme value theorem
) is a general result in
extreme value theory
regarding asymptotic distribution of extreme
order statistics
. The maximum of a sample of
iid
random variables
after proper renormalization can only
converge in distribution
to one of 3 possible distributions, the
Gumbel distribution
, the
Fréchet distribution
, or the
Weibull distribution
. Credit for the extreme value theorem (or convergence to types theorem) is given to
Gnedenko
(1948), previous versions were stated by
Ronald Fisher
and
Leonard Henry Caleb Tippett
in 1928 and
Fréchet
in 1927.
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