Re: Statistics problem from a programmer
From: Robert Dodier (robert_dodier_at_yahoo.com)
Date: 10/30/04
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Date: 29 Oct 2004 19:10:27 -0700
freddiemac <freddie@mac.com> wrote:
> Say I have a range 0-T
> There exist N datapoints within this range, with a pseudo-random
> distribution.
> If I wanted to be reasonably sure (S%) that all the data points N fall
> below a certain level L, how would I go about finding S%?
> Otherwise, can I calculate for a level L what surety S% that all N will
> fall below?
Well, all points are less than L iff the greatest of them is less than L.
The distribution of the greatest of an independent, identically
distributed sample of N items, it turns out, is equal to
F(x)^N
where F(x) is the cumulative distribution function.
(If independent but not identical, it's F1(x) F2(x) F3(x) ... FN(x).)
If I understand your question, S% = F(L)^N.
If you know S% and you want to calculate L, you can
invert the equation. Solving it might mean using a numerical method,
maybe something as simple as making a look-up table and seeing
where F(L)^N is approximately equal to S%.
What's the distribution in question?
Hth,
Robert Dodier
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