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Re: st: create unique random number variable


From   Joerg Luedicke <joerg.luedicke@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: create unique random number variable
Date   Tue, 24 Apr 2012 11:04:26 -0700

On further thought, the problem does not seem to be the mixture per
se. Of course, we can have a mixture with as many components as we
have data points, and that would still be essentially the same as just
drawing once. For example, we could type:

*---------
clear
set obs 100

gen p1=runiform() in 1
forval i=2/100 {
	replace p1=runiform() in `i'
}
*---------

and this would still be equivalent to:

*---------
gen p2=runiform()
*---------

However, drawing again in case of ties may depend on the density of
the uniformly distributed data points because ties are more likely to
appear in regions (however defined) with higher density and the
suggested algorithm then searches for values which are more likely to
appear in regions with lower density, which seems to be the reason for
the distribution being smoother as compared to the original draw.

J.


On Tue, Apr 24, 2012 at 10:19 AM, Joerg Luedicke
<joerg.luedicke@gmail.com> wrote:
> Stas,
>
> Just out of curiosity: could following this approach still be
> described as a strictly random draw (of course, 'strictly' in terms of
> pseudo-randomness) from a uniform distribution? Because what
> essentially happens is that the randomly emerging ties are filled in
> with yet another draw from the uniform. As a consequence, the
> resulting integers are drawn from a mixture of several or many uniform
> distributions. The component probabilities itself then depend on
> randomly emerging ties, so it should not make much different in
> practice. However, the resulting distribution looks somewhat smoother
> than one might expect (due to being a mixture of k uniforms, I
> presume). Compare the following histograms before and after the
> redraws (for which I modified your code):
>
>
> //draw from uniform (0,1)
> clear
> set obs 1000000
> set seed 1234
> generate uu =runiform()
> hist uu, name(unif, replace) bin(1000)
>
> //mapped to integers
> clear
> set obs 1000000
> set seed 1234
> generate uu = int(1500000*uniform())
> bysort uu: generate byte nonuniq = _n > 1
> hist uu, name(g0, replace) bin(1000)
>
> //drawing again in case of ties
> sum nonuniq
> while r(max) > 0 {
> bysort uu: replace uu = int(1500000*uniform()) if _n > 1
> bysort uu: replace nonuniq = _n > 1
> sum nonuniq, mean
> }
> hist uu, name(g1, replace) bin(1000)
>
> So I don't know what OP's demands are with regard to 'randomness', but
> maybe this could matter in some applications? (Perhaps in rocket
> science :)  )
>
> J.
>
>
> On Tue, Apr 24, 2012 at 7:43 AM, Stas Kolenikov <skolenik@gmail.com> wrote:
>> On Tue, Apr 24, 2012 at 4:37 AM, raoul reulen <r.c.reulen@gmail.com> wrote:
>>> Hello
>>>
>>> I'm trying to generate a random number variable like this:
>>>
>>> .set seed 12345
>>> .gen x = int(1000*uniform())
>>>
>>> However, the random numbers in variable x are not unique. Is there a
>>> way to ensure they are unique?
>>
>> clear
>> set obs 400
>> * this is your sample size
>>
>> generate uu = int(1000*uniform())
>> bysort uu: generate byte nonuniq = _n > 1
>> sum nonuniq, mean
>> while r(max) > 0 {
>> bysort uu: replace uu = int(1000*uniform()) if _n > 1
>> bysort uu: replace nonuniq = _n > 1
>> sum nonuniq, mean
>> }
>> drop nonuniq
>>
>> --
>> Stas Kolenikov, also found at http://stas.kolenikov.name
>> Small print: I use this email account for mailing lists only.
>> *
>> *   For searches and help try:
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>> *   http://www.ats.ucla.edu/stat/stata/

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