Re: Idempotence and "Replication Insensitivity" are equivalent ?

The median, like the mean IS an aggregate function.

All dbms implements it.

Further, it is formally like a "mean" in fact. Conceptually they are both a syntesis of the distribution:

the AVG is the value which minimize the sum of square differences

ie. sum | xi - c | ^ 2 is minimum for c = AVG()

the Median is the value which minimize the sum of absolute differences

ie. sum | xi - c | is minimum for c = MEDIAN()

If AVG() is an aggregate function, it is absolutely meaningles not to consider the MEDIAN() as an aggregate function.

Actually, every statistics obtained by minimizing

    sum | xi - c | ^ k

makes sense as an aggregate function.

In fact we also have that

for k->-infinity c = MIN(), and for k->+infinity c=MAX()

If your model is not able to mode, the MEDIAN as an aggregate function, it's not a good model. Nor consistent. Nor useful in practice.

-P

Aloha Kakuikanu ha scritto:

> pamelafluente_at_libero.it wrote:
> > ... but in case of a Median date, how would you proceed?
> > Would it be all "postprocessing" ?
>
> There is no such thing as mediant aggregate function. The only
> aggregate functions are "sum" and "min/max". All the rest deduces to
> these. The long list that Val referred to is nothing more than
> marketing brochure.
Received on Sat Sep 23 2006 - 02:18:37 CEST