Nonuniform PRNG?

[Richard Damon]

On 12/7/22 2:37 PM, David Lowry-Duda wrote:
> On Wed, Dec 07, 2022 at 03:28:47PM -0300, Sabrina Almodóvar wrote:
>> As far as I know, the state-of-the-art in statistical tests against 
>> PRNGs is the TestU01 library, available at
>>
>>  http://simul.iro.umontreal.ca/testu01/tu01.html
>
> I'm familiar with this type of test. But as far as I can tell and have 
> seen, these tests only tst against *uniform* PRNGs. I am not aware of 
> any written tests against nonuniform PRNGs.
>
> I suspect it would be possible to mirror a lot of the ideas. For 
> example, one common PRNG statistical test is to make many of matrices 
> of various sizes and to study the ranks of these matrices. Presumably 
> one could do a similar statistical analysis against what would be 
> expected for any particular probability distribution. Running a 
> candidate PRNG through this test will produce some sort of 
> distribution, after all.
>
> But it would be much nicer if work on statistical tests against 
> nonuniform PRNGs had already been done somewhere.
>
The big problem is there are MANY variations of nonuniform random 
numbers, and all the variations lead to different statistics to test 
against.

Most of the test can probably apply, but the new test criteria would 
need to be computed based on computing the exected results and expected 
variation in that result, largely based on various cross correlations of 
the numbers.

-- 
Richard Damon