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

From: <pamelafluente_at_libero.it>
Date: 25 Sep 2006 08:45:44 -0700

I see what you mean.

-P

vc ha scritto:

> 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?

```>
```

> Consider for example logarithmic(base 10) measurement scaling: (10,
> 100, 1000, 10000) -> (1,2,3,4). Or income adjusted for inflation, or
> any kind of data transformation.
```>

> > 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 - 17:45:44 CEST

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