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beta

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beta#

Generates beta distributed random numbers.

Description

The beta class object is used in the generate function to provide random numbers with beta distribution that has 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:

\[\begin{split}f_{p, q, \alpha, \beta}(x) = \left\{ \begin{array}{rcl} \frac{1}{B(p, q) * \beta^{p + q - 1}}(x - a)^{p - 1}*(\beta + \alpha - x)^{q - 1}, \alpha \leq x < \alpha + \beta \\ 0, x < \alpha, x \ge \alpha + \beta \end{array}\right.\end{split}\]

The cumulative distribution function is as follows:

\[\begin{split}F_{a, b}(x) = \left\{ \begin{array}{rcl} 0, x < \alpha \\ \int^x_{\alpha}\frac{1}{B(p, q) * \beta^{p + q - 1}}(y - \alpha)^{p - 1}*(\beta + \alpha - y)^{q - 1}dy, \alpha \leq x < \alpha + \beta, x \in R \\ 1, x \ge \alpha + \beta \end{array}\right.\end{split}\]

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

class beta#

Syntax

namespace oneapi::math::rng::device {
  template<typename RealType, typename Method>
  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;
    std::size_t count_rejected_numbers() const;
  };
}

Template parameters

typename RealType

Type of the produced values. Supported types:

  • float

  • double

typename Method

Generation method. The type is unspecified.

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 scale parameter \(\beta\)

size_t count_rejected_numbers() const

Method to obtain amount of random numbers that were rejected during the last generate function call. If no generate calls, 0 is returned.

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 = 1.0, \(\alpha\) = 0.0, \(\beta\) = 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 scale parameter.

Throws

oneapi::math::invalid_argument

Exception is thrown when \(p \leq 0\), or \(q \leq 0\), or \(\beta \leq 0\)

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 \(\beta\) - scale parameter value.

std::size_t beta::count_rejected_numbers() const

Return Value

Returns the amount of random numbers that were rejected during the last generate function call. If no generate calls, 0 is returned.

Parent topic: Device Distributions

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