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

Date: 25 Sep 2006 08:19:04 -0700

Message-ID: <1159197544.312807.105790_at_i3g2000cwc.googlegroups.com>

pamelafluente_at_libero.it wrote:

*> vc ha scritto:
*

> > [...]

*> > > In order to have a unique solution (and therefore equivalence), in the
**> > > case we are dealing with finite set of numbers when the cardinality is
**> > > not odd, the definition of MEDIAN is "completed" by *assuming* (it's
**> > > an ASSUMPTION, a convention) as median the average of the 2 central
**> > > terms of the ordered sequence of numbers:
**> > >
**> > > MEDIAN = ( x(n\2) + x(n\2 + 1) ) / 2
**> >
**> > The convention, while convenient in many cases, does not work if we
**> > want to preserve invariance to monotonic transformations. Considering
**> > the entire interval as the median is the only way to preserve the
**> > invariance property.
**>
**> I have simply recalled the standard definition,
**> but I have some "feeling" that this can be an interesting point.
**>
**> Can you make an example of what you have exactly in mind?
*

> Stated so generally it's not clear (to me) what you are referring to.

*> Invariance is sometimes used with different meanings,
**> eg, in the case of the variance we say that it is
**> translation-invariant.
**> What kind of "invariance" have you in mind ?
*

Let X is a randon variable, f is a transformation function and m is the median. Then median invariance would mean that m(f(X)) = f(m(X)). Received on Mon Sep 25 2006 - 17:19:04 CEST