in reply to Re: Unexpected under-dispersion in random simulations
in thread Unexpected under-dispersion in random simulations

I have tried using Math::Random::MT::Auto but the results were similar.
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Re^3: Unexpected under-dispersion in random simulations
by GrandFather (Saint) on Nov 30, 2010 at 19:57 UTC

    In that case the fault is in your code unless Math::Random::MT::Auto is a bad implementation. You could try Math::Random::MT instead which, on a cursory inspection, should pretty much be a drop in replacement. The Mersenne Twister is an excellent PNG for most purposes.

    True laziness is hard work
[reply]

      blakew hit the nail on the head.

      The distribution doesn't move from the realms of Binomial to Poisson until the ratio of events to probablities gets much lower than the 10:1 in the OPs example.

      Increasing the size of the circle, and/or reducing the size of the ranges--eg. 10,000 & 10 respectively--and the expect behaviour starts to manifest.

      This is true for the MT and even Windows default 15-bit rand() respectively:

      C:\test>874353 -M=10e3 -R=10
 10000:  0.100  0.098
0.1002 0.098369796979698

C:\test>874353 -M=10e3 -R=10
 10000:  0.102  0.101
0.1024 0.100724312431243

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