Contents

hypergeometric

Class is used for generation of hypergeometrically distributed integer types random numbers.

Description

The class object is used in the oneapi::mkl::rng::generate() function to provide random numbers hypergeometrically distributed with lot size \(l\), size of sampling \(s\), and number of marked elements in the lot \(m\), where \(l, m, s \in N \bigcup \{0\}; l \ge max (s, m)\).

Consider a lot of \(l\) elements comprising \(m\) marked and \(l\) - \(m\) unmarked elements. A trial sampling without replacement of exactly \(s\) elements from this lot helps to define the hypergeometric distribution, which is the probability that the group of \(s\) elements contains exactly \(k\) marked elements.

The probability distribution is given by:

\[P_(X = k) = \frac{C^k_mC^{s-k}_{l-m}}{C^s_l}, k \in \{max(0, s + m - l), ... , min(s, m)\}.\]

The cumulative distribution function is as follows:

\[\begin{split}F_{l, s, m}(x) = \left\{ \begin{array}{rcl} 0, x < max(0, s + m - l) \\ \sum^{\lfloor x \rfloor}_{k = max(0, s + m - l)}\frac{C^k_mC^{s-k}_{l-m}}{C^s_l}, max(0, s + m - l) \leq x \leq min(s, m) \\ 1, x > min(s, m) \end{array}\right.\end{split}\]

class hypergeometric

Syntax

namespace oneapi::mkl::rng {
template<typename IntType = std::int32_t, typename Method = hypergeometric_method::by_default>
class hypergeometric {
public:
    using method_type = Method;
    using result_type = IntType;
    hypergeometric();
    explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m);
    std::int32_t s() const;
    std::int32_t m() const;
    std::int32_t l() const;
};
}

Template parameters

typename IntType
Type of the produced values. Supported types:

  • std::int32_t

  • std::uint32_t

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

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

  • oneapi::mkl::rng::hypergeometric_method::by_default

  • oneapi::mkl::rng::hypergeometric_method::h2pe

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

hypergeometric()

Default constructor

explicit hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m)

Constructor with parameters

std::int32_t s() const

Method to obtain lot size

std::int32_t m() const

Method to obtain size of sampling without replacement

std::int32_t l() const

Method to obtain number of marked elements

Member types

hypergeometric::method_type = Method

Description

The type which defines transformation method for generation.

hypergeometric::result_type = IntType

Description

The type which defines type of generated random numbers.

Constructors

hypergeometric::hypergeometric()

Description

Default constructor for distribution, parameters set as l = 1, s = 1, m = 1.

explicit hypergeometric::hypergeometric(std::int32_t l, std::int32_T s, std::int32_T m)

Description

Constructor with parameters. l is a lot size, s is a size of sampling without replacement, m is a number of marked elements.

Throws

oneapi::mkl::invalid_argument

Exception is thrown when \(s < 0\), or \(m < 0\), or \(l < (s > m ? s : m)\)

Characteristics

std::int32_t hypergeometric::l() const

Return Value

Returns the distribution parameter l - lot size value.

std::int32_t hypergeometric::s() const

Return Value

Returns the distribution parameter s - size of sampling without replacement.

std::int32_t hypergeometric::m() const

Return Value

Returns the distribution parameter m - number of marked elements.

Parent topic: Distributions

binomial poisson