.rst .pdf

open issue suggest edit

Contents

beta

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

Description

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

The probability distribution is given by:

$$\begin{array}{r}{f}_{p,q,\alpha ,\beta }(x)=\{\begin{array}{r}\frac{1}{B(p,q)\ast {\beta }^{p+q-1}}(x-a{)}^{p-1}\ast (\beta +\alpha -x{)}^{q-1},\alpha \le x<\alpha +\beta \\ 0,x<\alpha ,x\ge \alpha +\beta \end{array}\end{array}$$

The cumulative distribution function is as follows:

$$\begin{array}{r}{F}_{a,b}(x)=\{\begin{array}{r}0,x<\alpha \\ {\int }_{\alpha }^x\frac{1}{B(p,q)\ast {\beta }^{p+q-1}}(y-\alpha {)}^{p-1}\ast (\beta +\alpha -y{)}^{q-1}dy,\alpha \le x<\alpha +\beta ,x\in R\\ 1,x\ge \alpha +\beta \end{array}\end{array}$$

Where $B(p,1)$ is the complete beta function.

class beta

Syntax

namespace oneapi::mkl::rng {
template<typename RealType = float, typename Method = beta_method::by_default>
class beta {
public:
    using method_type = Method;
    using result_type = RealType;
    beta();
    explicit beta(RealType p, RealType q, RealType a, RealType b);
    RealType p() const;
    RealType q() const;
    RealType a() const;
    RealType b() const;
};
}

Template parameters

typename RealType

Type of the produced values. Supported types:

• float

• double

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

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

• oneapi::mkl::rng::beta_method::by_default

• oneapi::mkl::rng::beta_method::cja

• oneapi::mkl::rng::beta_method::cja_accurate

See description of the methods in Distributions methods template parameter.

Class Members

Routine	Description
beta()	Default constructor
explicit beta(RealType p, RealType q, RealType a, RealType b)	Constructor with parameters
RealType p() const	Method to obtain shape p
RealType q() const	Method to obtain shape q
RealType a() const	Method to obtain displacement $\alpha$
RealType b() const	Method to obtain scalefactor $\beta$

Member types

beta::method_type = Method

Description

The type which defines transformation method for generation.

beta::result_type = RealType

Description

The type which defines type of generated random numbers.

Constructors

beta::beta()

Description

Default constructor for distribution, parameters set as p = 1.0, q = 0.0, $\alpha$ = 1.0, $\beta$ = 1.0.

explicit beta::beta(RealType p, RealType q, RealType a, RealType b)

Description

Constructor with parameters. p and q are shapes, $\alpha$ is a displacement, $\beta$ is a scalefactor.

Throws

oneapi::mkl::invalid_argument

Exception is thrown when $p\le 0.0f$, or $q\le 0.0f$, or $\beta \le 0.0f$

Characteristics

RealType beta::p() const

Return Value

Returns the distribution parameter p - shape.

RealType beta::q() const

Return Value

Returns the distribution parameter q - shape.

RealType beta::a() const

Return Value

Returns the distribution parameter $\alpha$ - displacement.

RealType beta::b() const

Return Value

Returns the distribution parameter $\beta$ - scalefactor.

Parent topic: Distributions

previous

gamma

next

chi_square