oneapi::mkl::rng::device::poisson

Generates Poisson distributed random values.

Syntax

template<typename IntType, typename Method>
class poisson {
public:
using method_type = Method;
using result_type = IntType;
poisson(): poisson(0.5){} explicit poisson(double lambda);
explicit poisson(const param_type& pt);
double lambda() const;
param_type param() const;
void param(const param_type& pt);
};

Include Files

  • oneapi/mkl/rng/device.hpp

Description

The oneapi::mkl::rng::device::poisson class object is used in the oneapi::mkl::rng::device::generate function to provide Poisson distributed random numbers with distribution parameter λ, where λ∈R; λ > 0.

The probability distribution is given by:

P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!}

:math`k in {0, 1, 2, ldots }`. The cumulative distribution function is as follows:

F_{\lambda}(x) = \begin{cases} \sum_{k=0}^{\lfloor x \rfloor} \frac{\lambda^k e^{-\lambda}}{k!}, & x \geq 0 \\ 0, & x < 0 \end{cases}, x \in R

Template Parameters

typename IntType

Type of the produced values. The specific values are as follows:

std::int32_t

std::uint32_t

typename Method

Generation method. The specific values are as follows:

oneapi::mkl::rng::device::poisson_method::devroye

Note

The Poisson oneapi::mkl::rng::device::poisson_method::devroye method uses the following underlying methods depending on the lambda parameter:
  • table-lookup method for small lambdas (\lambda < 60)

  • Devroye’s method [Devroye] for medium lambdas (60 \leq \lambda < 1000)

  • Gaussian approximation for huge lambdas (\lambda \geq 1000)

Input Parameters

Name

Type

Description

lambda

double

Distribution parameter λ.