celeritas::PoissonDistribution< RealType > Class Template Reference

Sample from a Poisson distribution. More...

#include <PoissonDistribution.hh>

Public Types
Type aliases
using	real_type = RealType
using	result_type = unsigned int

Public Member Functions
CELER_FUNCTION	PoissonDistribution (real_type lambda=1)
	Construct from the mean of the Poisson distribution.
template<class Generator >
CELER_FUNCTION result_type	operator() (Generator &rng)
template<class Generator >
CELER_FUNCTION auto	operator() (Generator &rng) -> result_type
	Sample a random number according to the distribution.

Static Public Member Functions
static CELER_CONSTEXPR_FUNCTION int	lambda_threshold ()
	Maximum value of lambda for using the direct method.

Detailed Description

template<class RealType = ::celeritas::real_type>
class celeritas::PoissonDistribution< RealType >

Sample from a Poisson distribution.

The Poisson distribution describes the probability of \( k \) events occuring in a fixed interval given a mean rate of occurance \( \lambda \) and has the PMF:

\[ f(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!} \:. \]

For small \( \lambda \), a direct method described in Knuth, Donald E., Seminumerical Algorithms, The Art of Computer Programming, Volume 2 can be used to generate samples from the Poisson distribution. Uniformly distributed random numbers are generated until the relation

\[ \prod_{k = 1}^n U_k \le e^{-\lambda} \]

is satisfied; then, the random variable \( X = n - 1 \) will have a Poisson distribution. On average this approach requires the generation of \( \lambda + 1 \) uniform random samples, so a different method should be used for large \( \lambda \).

Geant4 uses Knuth's algorithm for \( \lambda \le 16 \) and a Gaussian approximation for \( \lambda > 16 \) (see G4Poisson), which is faster but less accurate than other methods. The same approach is used here.

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The documentation for this class was generated from the following file:

• PoissonDistribution.hh