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
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