# weibull¶

Class is used for generation of Weibull distributed real types random numbers.

Description

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

The probability distribution is given by:

$\begin{split}f_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \frac{\alpha}{\beta^\alpha}(x - a)^{\alpha - 1}exp((-\frac{x - a}{\beta})^{\alpha}), x \ge a \\ 0, x < a \end{array}\right.\end{split}$

The cumulative distribution function is as follows:

$\begin{split}F_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} 1 - exp((-\frac{x - a}{\beta})^{\alpha}), x \ge a \\ 0, x < a \end{array}\right.\end{split}$

## class weibull¶

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();
explicit weibull(RealType alpha, RealType a, RealType b);
RealType alpha() const;
RealType a() const;
RealType beta() const;
};
}


Template parameters

typename RealType
Type of the produced values. Supported types:
• float

• double

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

Transformation method, which will be used for generation. Supported types:

• oneapi::mkl::rng::weibull_method::by_default

• oneapi::mkl::rng::weibull_method::icdf

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

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

weibull()

Default constructor

explicit weibull(RealType alpha, RealType a, RealType beta)

Constructor with parameters

RealType alpha() const

Method to obtain shape value

RealType a() const

Method to obtain displacement value

RealType beta() const

Method to obtain scalefactor value

Member types

weibull::method_type = Method


Description

The type which defines transformation method for generation.

weibull::result_type = RealType


Description

The type which defines type of generated random numbers.

Constructors

weibull::weibull()


Description

Default constructor for distribution, parameters set as alpha = 1.0, a = 0.0, and b = 1.0.

explicit weibull::weibull(RealType alpha, RealType a, RealType beta)


Description

Constructor with parameters. alpha is a shape value, a is a displacement value, beta is a scalefactor value.

Throws

oneapi::mkl::invalid_argument

Exception is thrown when $$alpha \leq$$ static_cast<RealType>(0.0), or $$beta \leq$$ static_cast<RealType>(0.0)

Characteristics

RealType weibull::alpha() const


Return Value

Returns the distribution parameter alpha - shape value.

RealType weibull::a() const


Return Value

Returns the distribution parameter a - displacement value.

RealType weibull::beta() const


Return Value

Returns the distribution parameter beta - scalefactor value.

Parent topic: Distributions