Hi!
I'm looking at an article that references a result by Fisher & Tippett
(specific reference is "Limiting Forms of the Frequency Distribution of the
Largest or Smallest Member of a Sample," Procedings of the Cambridge
Philosophical Society 24, 180-190 (1928)). The article presents the result as
follows: if there are S independent samples of size m from a parent population
bounded below by a, and if xi is the smallest value in sample i, then the
limiting distribution of the minimum of the xi-values is Weibull with location
parameter a as m -> infinity.
This seems like a not particularly rigorous description of the result, and I
wanted to read the original statement to make sure that all the details are
covered here, i.e. it seems like the parent distribution would have to be
continuous, at least, and that a should be the greatest lower bound rather than
just a bound. So, I ordered the original article from my library and have been
waiting a loooong time with no success. So... can anyone help me out with a
precise statement regarding this result? (If it helps, I have obtained
Gumbel's "Statistics of Extremes" to see if it's buried in there, but so far
haven't found it. Page number?)
Thanks in advance.
Tom McWilliams
Decision Sciences Dept, Drexel U.
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