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gumbel

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gumbel#

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

Description

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

The probability distribution is given by:

\[f_{a, \beta}(x) = \frac{1}{\beta}exp(-\frac{x - a}{\beta})exp(-exp(\frac{x - a}{\beta})), x \in R.\]

The cumulative distribution function is as follows:

\[F_{a, \beta}(x) = 1 - exp(-exp(\frac{x - a}{\beta})), x \in R.\]

class gumbel#

Syntax

namespace oneapi::math::rng {
template<typename RealType = float, typename Method = gumbel_method::by_default>
class gumbel {
public:
    using method_type = Method;
    using result_type = RealType;
    gumbel();
    explicit gumbel(RealType a, RealType b);
    RealType a() const;
    RealType b() const;
};
}

Template parameters

typename RealType
Type of the produced values. Supported types:

  • float

  • double

typename Method = oneapi::math::rng::gumbel_method::by_default

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

  • oneapi::math::rng::gumbel_method::by_default

  • oneapi::math::rng::gumbel_method::icdf

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

gumbel()

Default constructor

explicit gumbel(RealType a, RealType b)

Constructor with parameters

RealType a() const

Method to obtain displacement value

RealType b() const

Method to obtain scalefactor value

Member types

gumbel::method_type = Method

Description

The type which defines transformation method for generation.

gumbel::result_type = RealType

Description

The type which defines type of generated random numbers.

Constructors

gumbel::gumbel()

Description

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

explicit gumbel::gumbel(RealType a, RealType b)

Description

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

Throws

oneapi::math::invalid_argument

Exception is thrown when \(b \leq\) static_cast<RealType>(0.0)

Characteristics

RealType gumbel::a() const

Return Value

Returns the distribution parameter a - displacement value.

RealType gumbel::b() const

Return Value

Returns the distribution parameter b - scalefactor value.

Parent topic: Host Distributions

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