Generates random numbers with negative binomial distribution.


template<typename IntType = std::int32_t, typename Method = negative_binomial_method::by_default>
class negative_binomial {
using method_type = Method;
using result_type = IntType;
negative_binomial(): negative_binomial(0.1, 0.5){}
explicit negative_binomial(double a, double p);
double a() const;
double p() const;

Devices supported: Host and CPU

Include Files

  • oneapi/mkl/rng.hpp


The oneapi::mkl::rng::negative_binomial class object is used in the oneapi::mkl::rng::generate function to provide random numbers with negative binomial distribution and distribution parameters a and p, where p, aR; 0 < p < 1; a > 0.

If the first distribution parameter aN, this distribution is the same as Pascal distribution. If aN, the distribution can be interpreted as the expected time of a-th success in a sequence of Bernoulli trials, when the probability of success is p.

The probability distribution is given by:


The cumulative distribution function is as follows:


Intel’s compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice. Notice revision #20110804

This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.

Template Parameters

typename IntType = std::int32_t

Type of the produced values. The specific values are as follows: std::int32_t std::uint32_t

typename Method =  oneapi::mkl::rng::negative_binomial_method::by_default

Generation method. The specific values are as follows: oneapi::mkl::rng::negative_binomial_method::nbar See brief descriptions of the methods in Distributions Template Parameter Method Values

Input Parameters






The first distribution parameter a.



The second distribution parameter p.