poisson#

Generates Poisson distributed random values.

Description#

The poisson class object is used in the generate function to provide Poisson distributed random numbers with distribution parameter λ, where \(\lambda \in R; \lambda > 0\).

The probability distribution is given by:

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

\(k \in \{0, 1, 2, \ldots \}\).

The cumulative distribution function is as follows:

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

API#

Syntax#

namespace oneapi::mkl::rng::device {
  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

Template Parameters#

typename Type

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

  • std::int32_t

  • std::int64_t

typename Method

Generation method. The specific values are as follows:

  • oneapi::mkl::rng::device::poisson_method::by_default

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

See brief descriptions of the methods in Distributions Template Parameter Method.

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.