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Luc Maisonobe commented on MATH197:

The problems comes from the way the distribution is computed. A Poisson process is simulated
and lots of random numbers are drawn, until there product reach some threshold.
If lambda is greater or equal to 746, the value of Math.exp(lambda) cannot be represented
anymore in a double and it is replaced by 0 (exactly 0). The previous value, for lambda =
745 is 4.9e324, which is ... small.
In this case, the threshold is never reached and the loop is exited only because of an exceeded
count.
This means that in addition to being long to obtain, the result is false (it will be exactly
1000 * lambda).
So the current algorithm cannot handle large lambda values.
Does anybody have a reference for another algorithm that could be used for large lambda values
?
> RandomDataImpl.nextPoisson() is extreme slow for large lambdas
> 
>
> Key: MATH197
> URL: https://issues.apache.org/jira/browse/MATH197
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 1.2
> Environment: jdk1.6.0_04, windows xp
> Reporter: Tolja Zubow
>
> The RandomDataImpl.nextPoisson() is extreme slow for large lambdas:
> E.g. drawing 100 random numbers with lambda = 1000 takes around 10s on my dual core with
2.2GHz.
> With lambda smaller than 500 everything is fine. Any ideas?
> RandomDataImpl r = new RandomDataImpl();
> r.reSeed(101);
> int d = 100;
> long poissonLambda = 1000;
> long st = System.currentTimeMillis();
> for (int row = 0; row < d; row++) {
> long nxtRnd = r.nextPoisson(poissonLambda);
> }
> System.out.println("delta " + (System.currentTimeMillis()  st));

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