randommontecarlomersenne-twister

Testing the quality of PRNGs

I am playing around with PRNGs (like Mersenne Twister and rand() function of stdlib) and I would want a good test that would help me ascertain the quality of random data produced by the PRNGs. I have calculated the value of Pi using random numbers generated by the PRNGs, and I find rand() and Mersenne Twister to be very close to offer a distinction (do I need to scrutinize after 10 decimal points?).

I do not have much idea about Monte Carlo simulations; please let me know about some algorithm/application (possibly something simple yet which could provide good inferences) that would help me distinguish them in terms of quality.

EDIT 1: I didn't notice before, but there is a similar thread: How to test random numbers?

EDIT 2: I am not able to interprete the results of NIST, as mentioned in one of the comments. I got this idea of visually interpreting the pattern (if any) from random.org and am following that because of it's simplicity. I would be very glad if someone could comment on the process of my testing:

  1. Generate N randoms from [0,1] using rand() and MT1997
  2. if (round(genrand_real1() / rand_0_1())) then red pixel, else black

As I understand that this is not a very precise solution, but if this provides a reasonable estimate, then I could live with this at the present moment.

Solution

  • There are two standard test suites for testing random numbers.

    1. NIST test suite. They have an implementation in C.
    2. Diehard Test Suite (developed by George Marsaglia). There is a C library implementation of these tests.

    There is a R interface to the Dieharder library, called RDieHarder. This library provides an interface to both the NIST and Diehard test suites.