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Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: vc <>
Date: 26 Sep 2006 08:18:20 -0700
Message-ID: <> wrote:
> 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)) ?

log(X): {1, 2, 3, 4}, m(log(X)): [2, 3] m(X) : [100, 1000], log(m(X)) : [2, 3]

> Descriptive statistics, and the median concept exist independently of
> the notion of probability measure (where they get generalized).

Sorry but that is obviously a nonsensical statement. Statistics is not a collection of tricks that one can apply to data and come up with an answer. Learning probability is a precondition to understanding statistical methods which otherwise may look as a meaningless number game. First, one starts with the notions like a random experiment, sample space S and probability P; then, one moves to the idea of random variable, a random sample of size n, and other statistical stuff. Your elementary school curriculum may be different though.

>Of course any set of distinct values can be seen as a uniform discrete
> distribution, but that is not necessary.

That statement does not make any obvious sense.

> -P
Received on Tue Sep 26 2006 - 10:18:20 CDT

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