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SubjectRe: Interesting scheduling times - NOT
On Tue, Sep 22, 1998 at 11:18:53AM +0200, Peter T. Breuer wrote:
> Eh? does anyone know the statistics of the MINIMUM result from N normally
> distributed tests?
>
> I don't, but since the minimum comes from the tail, it is a rare event
> and hence its variance must be large.
>
> Your result is what I would naively expect from a normal curve, but I don't
> believe you have a normal curve. Negative times are impossible :-).
> You must have a quantized distribution (nano seconds?) with a tail
> at 0 and +oo. I suppose it's m*exp(-x/m) or something. Can you run
> some monte carlo simulations with that to get an idea of the distribution of
> the _minimum_?

Well, if we had a normal (or Binomial) distribution and make 1000 tests, we
lokk for the Variance of the 0.001 quantil. I don't have a formula in mind
for this, but, yes, the variance would be quite large. I guess in the order
of \sigma^2 (instead of \frac{\sigma^2}{n} for the average).

We certainly have a true minimum value mv (the number of unavoidable CPU
cycles) and the distribution is highly non-symmetric. I think shifted Poisson
Poi(x-mv) or exponential distributions are not the worst guess.
Richard wants to find the true minimum mv. The minimum measured is not the
worst estimator. It's even asymptotically unbiased. If you knew the
distribution you were of course able to find more efficient ones.

Reagrds,
--
Kurt Garloff, Dortmund
<K.Garloff@ping.de>
PGP key on http://student.physik.uni-dortmund.de/homepages/garloff
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