hypergeometric

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 $l, m, s \in N ⋃ {0}; l \geq m a x (s, m)$ .

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_{m}^{k} C_{l - m}^{s - k}}{C_{l}^{s}}, k \in {m a x (0, s + m - l), . . ., m i n (s, m)} .

The cumulative distribution function is as follows:

\begin{array}{r} F_{l, s, m} (x) = {\begin{array}{rcl} 0, x < m a x (0, s + m - l) \\ \sum_{k = m a x (0, s + m - l)}^{⌊ x ⌋} \frac{C_{m}^{k} C_{l - m}^{s - k}}{C_{l}^{s}}, m a x (0, s + m - l) \leq x \leq m i n (s, m) \\ 1, x > m i n (s, m) \end{array} \end{array}

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: Host Distributions

hypergeometric

Contents

hypergeometric#

class hypergeometric#