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