Re: [Gretl-users] powerball puzzle
On Mon, 5 Dec 2016, Sven Schreiber wrote:
Am 05.12.2016 um 22:31 schrieb Allin Cottrell:
> Yes, this seems to be an artifact coming from the fact that the vector
> of cumulated sorted relative white-ball frequencies is, so to speak,
> "super-uniform" -- much more uniform than a set of draws from U[0,1].
I still don't think this invented terminology is helpful (too Gaussian to be
Gaussian, super-uniform,... what's next :-)
I think we can give a meaning to this kind of talk.
<hansl>
nulldata 99
series u = index/100
series z = invcdf(N, u)
print u z -o
normtest z --swilk
</hansl>
The series u is "perfectly uniform" and after passing through the
inverse normal cdf it becomes "perfectly normal", getting a p-value
of 0.9999 on the Shapiro-Wilk test. However, it's clear that the
probability of u deriving from a true random U(0,1) generator is
essentially zero, as is the probability that the derived z could be
a random sample from a normal distribution.
This is obvious, I guess, but a standard normality test is _just_ a
test for following the normal distribution, and not a test for
whether a sequence could be a random sample from a normal
distribution -- not without the maintained hypothesis that the input
data are in fact random.
Allin