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

Date: 26 Sep 2006 08:56:54 -0700

Message-ID: <1159286214.872151.318240_at_h48g2000cwc.googlegroups.com>

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.

*>
*

> Nothing. If you do not define it.

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