weibull#

Generates Weibull distributed random numbers.

Description#

The weibull class object is used in the generate function to provide Weibull distributed random numbers with displacement a, scalefactor β, and shape \(\alpha\), where \(\alpha, \beta, a \in R ; \alpha > 0, \beta > 0\).

The probability density function is given by:

\[\begin{split}f_{a, \alpha, \beta}(x) = \begin{cases} \frac{\alpha}{\beta^\alpha} (x - a)^{\alpha - 1} \exp \left( - {\left( \frac{x-a}{\beta} \right)}^{\alpha} \right), & x \geq a \\ 0, & x < a \end{cases}\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{a, \alpha, \beta}(x) = \begin{cases} 1 - \exp \left( - {\left( \frac{x-a}{\beta} \right)}^{\alpha} \right), & x \geq a \\ 0, & x < a \end{cases}, - \infty < x < + \infty\end{split}\]

Product and Performance Information

Performance varies by use, configuration and other factors. Learn more at https://www.intel.com/PerformanceIndex. Notice revision #20201201

API#

Syntax#

namespace oneapi::mkl::rng {
template<typename RealType = float,
         typename Method = weibull_method::by_default>
class weibull {
public:
  using method_type = Method;
  using result_type = RealType;

  weibull(): weibull((Real_Type)1.0, (RealType)0.0, (RealType)1.0){}
  explicit weibull(RealType alpha, RealType a, RealType beta);
  explicit weibull(const param_type& pt);

  RealType alpha() const;
  RealType a() const;
  RealType beta() const;
  param_type param() const;
  void param(const param_type& pt);
};
}

Devices supported: CPU and GPU.

Include Files#

  • oneapi/mkl/rng.hpp

Template Parameters#

typename RealType = float

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

float

double

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

Generation method. The specific values are as follows: oneapi::mkl::rng::weibull_method::icdf

oneapi::mkl::rng::weibull_method::icdf_accurate

See brief descriptions of the methods in Distributions Template Parameter Method

Input Parameters#

Name

Type

Description

alpha

RealType (float, double)

Shape α

a

RealType (float, double)

Displacement a.

beta

RealType (float, double)

Scalefactor β.