# Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: vc <boston103_at_hotmail.com>
Date: 26 Sep 2006 08:56:54 -0700

pamelafluente_at_libero.it wrote:
> vc ha scritto:
>
> > pamelafluente_at_libero.it wrote:
> > > vc ha scritto:
> > >
> > > > pamelafluente_at_libero.it wrote:
> > > > > vc ha scritto:
> > > > ' m(f(x)) = f(m(x))' is a standard and very simple definition of
> > > > quantile invarince under monotonic transformations that can be found in
> > > > any statistics course.
> > >
> > > I know what is meant by saying that taking the interval between the 2
> > > central values is a way to preserve invariance wrt to monotonic trans,
> > > and I do agree with that, but.. the point is that you do not seem to be
> > > aware of the meaning of that statement
> > >
> > > Tell me what it means to you that an *Interval*, such as the median
> > > values, is invariant wrt to monotonic transf. Let's make an example
> > > with:
> > > 10 100 1000 10000 and Log. What does it mean to you that the median
> > > interval [100, 1000] is invariant wrt to Log transformation and how do
> > > you fit it in the expression m(f(x)) = f(m(x)) ?
> >
> > log(X): {1, 2, 3, 4}, m(log(X)): [2, 3]
> > m(X) : [100, 1000], log(m(X)) : [2, 3]
>
> 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 say so, that's OK with me.

[...]
> I just note that MEDIAN() is used by every DBA or user and they need
> to
> know nothing about probability measure.

>
> > >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.

>
> Here again our opinions are not coincident.
>
>
>
> Thanks for the instructive discussion :)
>
> -P
Received on Tue Sep 26 2006 - 17:56:54 CEST

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