Re: [Gretl-users] powerball puzzle
On Mon, 5 Dec 2016, Allin Cottrell wrote:
However, I'm now coming to the conclusion that there's no
obvious way (and
perhaps no way) to take the white-ball count data and turn it into something
that ought theoretically to be U(0,1) -- which would be step zero towards
applying the method just mentioned. I think Jack's point about failure of
independence is important: cumulating sorted relative count-frequencies will
give you a quantity that's distributed on [0,1] OK, but it won't act like a
set of independent random draws.
Well, there is one, but it's not straightforward. Each week's data is a
sample (without replacement) of 5 numbers out of 69, which gives you 69! /
(5! 64!) = 11238513 equiprobable drawings. If you find a way to sort them
according to some criterion (not difficult), then you have that your 605
observations come from a discrete uniform distribution; if you normalise
it to be between 0 and 1, then the support become so "tight", so to speak,
to resemble very closely a continuous U(0,1).
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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