Re: problem with rand ?

[Paul Kienzle]

Dimitri,

Running the simple birthday test on randn, I got 47 out of 100
trials with no duplicates instead of the expected 50, so it also
suffers the same problem.

Extending randn to 53 bits will take some thought.  No guarantees
I will get to it any time soon, so if anyone is inspired, please fix it.

- Paul

On Jul 27, 2004, at 11:46 PM, Dmitri A. Sergatskov wrote:

> I found that random series returned by rand (from octave-forge) returns
> a higher number of _identical_ values than I would expect:
>
> octave:1> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> any(dss1==0)
> ans = 1
> octave:2> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = [](1x0)
> octave:3> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = 60641
> octave:4> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = [](1x0)
> octave:5> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans =
>
>   26998  27604
>
> octave:6> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = 16034
> octave:7> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = 23032
> octave:8> s1=rand(1,128*1024); ss1=sort(s1); dss1=diff(ss1); 
> find(dss1==0)
> ans = 121716
>
> etc...
>
> I would think that for random 2^17 numbers probability of two identical
> numbers would be something like 2^17 / 2^54 (assuming ieee 64 bit 
> double
> representation)
>
> Matlab does not show this behavior even for larger series:
>
> >> s1=rand(1,256*1024); ss1=sort(s1); dss1=diff(ss1); any(dss1==0)
>
> ans =
>
>      0
>
> >> s1=rand(1,1024*1024); ss1=sort(s1); dss1=diff(ss1); any(dss1==0)
>
> ans =
>
>      0
>
> >> s1=rand(1,1024*1024); ss1=sort(s1); dss1=diff(ss1); any(dss1==0)
>
> ans =
>
>      0
>
> Am I missing something here?
>
> Sincerely,
>
> Dmitri.
>
>
>
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