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

Date: 26 Sep 2006 07:10:38 -0700

Message-ID: <1159279838.424542.241700_at_d34g2000cwd.googlegroups.com>

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)) ?

*> >
*

> > Further, we are not talking about median of rv's. But about median of a

*> > finite set of numerical values.
**>
**> The expression "median of a finite set of numerical values" does not
**> make any sense whatsoever unless such set is a random sample
**> realization of some observations/experiment.
*

Descriptive statistics, and the median concept exist independently of the notion of probability measure (where they get generalized). Of course any set of distinct values can be seen as a uniform discrete distribution, but that is not necessary.

-P Received on Tue Sep 26 2006 - 16:10:38 CEST