Re: Idempotence and "Replication Insensitivity" are equivalent ?
Date: 26 Sep 2006 07:10:38 -0700
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
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