gamma

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

Description

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

The probability distribution is given by:

\[\begin{split}f_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \frac{1}{\Gamma(\alpha)\beta^{\alpha}}(x - a)^{\alpha - 1}e^{-(x - a) / \beta}, x \ge a \\ 0, x < a \end{array}\right.\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{a, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \int^x_a\frac{1}{\Gamma(\alpha)\beta^{\alpha}}(y - a)^{\alpha - 1}e^{-(y - a) / \beta}dy, x \ge a \\ 0, x < a \end{array}\right.\end{split}\]

class gamma

Syntax

namespace oneapi::mkl::rng {
template<typename RealType = float, typename Method = gamma_method::by_default>
class gamma {
public:
    using method_type = Method;
    using result_type = RealType;
    gamma();
    explicit gamma(RealType alpha, RealType a, RealType beta);
    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::gamma_method::by_default

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

• oneapi::mkl::rng::gamma_method::by_default

• oneapi::mkl::rng::gamma_method::marsaglia

• oneapi::mkl::rng::gamma_method::marsaglia_accurate

See description of the methods in Distributions methods template parameter.

Class Members

Routine	Description
gamma()	Default constructor
explicit gamma(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 scale value

Member types

gamma::method_type = Method

Description

The type which defines transformation method for generation.

gamma::result_type = RealType

Description

The type which defines type of generated random numbers.

Constructors

gamma::gamma()

Description

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

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

Description

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

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 gamma::alpha() const

Return Value

Returns the distribution parameter alpha - shape value.

RealType gamma::a() const

Return Value

Returns the distribution parameter a - displacement value.

RealType gamma::beta() const

Return Value

Returns the distribution parameter beta - scale parameter.

Parent topic: Distributions