Major Description
The PoissonSampler is limited to returning an integer by the interface of the DiscreteSampler. As it stands an input mean above Integer.MAX_VALUE is allowed although it makes no sense as the Poisson distribution is significantly truncated.
The algorithm of the SmallMeanPoissonSampler sets a limit on the returned sample of Integer.MAX_VALUE. The algorithm is valid although run-time would be impractical due to the nature of the algorithm. However at high mean (>40) the end user is expected to use either the LargeMeanPoissonSampler directly or the PoissonSampler which chooses the appropriate large mean algorithm.
However the current LargeMeanPoissonSampler uses (int)Math.floor(mean) during initialisation and any mean above Integer.MAX_VALUE would therefore be unsupported.
I propose to add this to the constructor of each Poisson sampler:
if (mean > Integer.MAX_VALUE) { throw new IllegalArgumentException(mean + " > " + Integer.MAX_VALUE); }
with documentation
* @throws IllegalArgumentException if {@code mean <= 0} or {@code mean > }{@link Integer.MAX_VALUE}.
It is noted that the limit of Integer.MAX_VALUE would allow the samples to reflect the Poisson distribution below that level but truncate it above that level to represent the remaining cumulative histogram at the single point of Integer.MAX_VALUE. This maintains the functionality of the sampler within the contract of the integer value returned by DiscreteSampler.
In practice the Poisson distribution is unlikely to be used at such a high mean; in this case it is appropriate to use a Gaussian approximation to the Poisson.
Note: Currently there is no code coverage from tests for the LargeMeanPoissonSampler checking if the mean is <= 0. Tests should be added to check the constructor does throw when a bad mean is used.