[LON-CAPA-users] random_permutation, choosing the $seed
Peter Dencker
dencker at math.uni-luebeck.de
Mon Sep 1 04:45:00 EDT 2014
Hello, Gerd.
The given problem compares the procedures for lists with 2,3,4 and 5
elements running both procedures in each case 10000 times. (The number
10000 is not the number of the shuffled items.)
The shown tables are tables of absolute frequencies. An example using
the seed range 1 .. 1E8 is the following. (Choosing the seeds between 1
and 1E8 doesn't change the behavior.)
10000 random permutations of ABC counted:
shuffle permute
ABC 1670 2254
ACB 1661 1555
BAC 1609 1785
BCA 1728 1900
CAB 1653 1406
CBA 1679 1100
The difference in the number of, e.g., 'CBA' and 'ABC' in the right
column seems to be a systematic effect. I tried to express this by using
the term 'bias'.
- Peter
Am 01.09.2014 03:14, schrieb Gerd Kortemeyer:
> Hi Again,
>
> On Aug 31, 2014, at 8:59 PM, Gerd Kortemeyer <kortemey at msu.edu> wrote:
>
>>
>> The problem may be 1e10 as upper limit - that’s awfully big. While I am unable to verify this right now, I have a vague feeling that a 32-bit integer is expected inside &random_permutation(), and that weird things could happen with the overflows or “negatives.” Maybe try with 1e8 (which is smaller than 2^31) and see if the bias goes away.
>
> I am not sure what “bias” is in this context means, but I just noticed that your array appears to have 10,000 elements, which means there are 10,000! different permutations. Of course 10,000! >> 1e10, so with the a random seed between 1 and 1e10, you’ll never “hit” all possible permutations - is that the “bias”?
>
> - Gerd.
>
>
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--
Dr. Peter Dencker
wissenschaftl. Mitarbeiter
UNIVERSITÄT ZU LÜBECK
INSTITUT FÜR MATHEMATIK
Ratzeburger Allee 160
23562 Lübeck
Tel +49 451 500 4254
Fax +49 451 500 3373
dencker at math.uni-luebeck.de
www.math.uni-luebeck.de
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