Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: <>
Date: 26 Sep 2006 07:10:38 -0700
Message-ID: <>

vc ha scritto:

> 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

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