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Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: vc <boston103_at_hotmail.com>
Date: 26 Sep 2006 10:09:35 -0700
Message-ID: <1159290575.781937.172770@b28g2000cwb.googlegroups.com>

pamelafluente_at_libero.it wrote:
> vc ha scritto:
> > > Ah finally. That's just wanted you to get aware of:
> > > You say:
> > >
> > > m(X) : [100, 1000],
> > >
> > > therefore log(m(X)) is formally the same as log( [100, 1000] )
> > >
> > > what does log( [100, 1000] ) means ?
> >
> > It means what it has always meant in the elementary school: mapping
> > every point in the closed interval to its logarithm.
>
> If you take log(S) as a shorthand for the set of point { Log(x), with
> x in S } , you
> have proven that invariance does not hold for internal point.

Of course not, it holds though for the interval as a whole. That's exactly why the interval reduction to a single point is not suitable for monotone transformations.

>Just
> because
> the mapping, altought monotonic, and hence "order preserving", is not
> linear.
>
> "mapping every point in the closed interval to its logarithm"
>
> If you take for instance (100 + 1000) / 2 and you map to its logaritm
> you do not have an "invariant" point.

Why would you want to do that if invariance is important ?
>
> That was my discussion point, and actually you proved it on the first
> place.

>
>
> >
>
> > > I just note that MEDIAN() is used by every DBA or user and they need
> > > to
> > > know nothing about probability measure.
>
> The median of a finite set of number is defined elementarily, with no
> need to introduce the concept of probability.

The notion of median without knowing zip about probability is as useful as the notion of flogiston in modern chemistry but if you think otherwise that's OK.

> > > > >Of course any set of distinct values can be seen as a uniform discrete
> > > > > distribution, but that is not necessary.
> > > >
> > > > That statement does not make any obvious sense.
> > >
> > > It does to me. {1 2 5} can be seen as a uniform with masses equal to
> > > 1/3.
> >
> > How do you know ? Are you saying that three samples are sufficient to
> > draw a conclusion like that ? If so, it would be quite a revolution
> > in statistics, they do not need ridiculous stuff like the law of large
> > numbers and such any more.
>
> Forget about inference. I am talking of a discrete rv X which has a
> support made of
> 3 points.

If the r.v. "support", or in more human language, sample space consists of three points and that's all you know about the r.v., how do you know what probabilities you can assign to those point ? By divine inspiration ? Received on Tue Sep 26 2006 - 12:09:35 CDT

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