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:
|
typename Method |
Generation method. The specific values are as follows:
See brief descriptions of the methods in Distributions Template Parameter Method. |
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. |