# multinomial¶

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

Description

The class object is used in the oneapi::mkl::rng::generate() function to provide n random numbers multinomially distributed, with independent trials $$(ntrial, m)$$ and possible mutually exclusive outcomes $$k$$, with corresponding probabilities $$p_i$$, where $$p_i \in R; 0 \leq p_i \leq 1; m, k \in N$$.

The probability distribution is given by:

$P(X_1 = x_1, ..., X_k = x_k) = \frac{m!}{\Pi^k_{i = 1}x_i!}\Pi^k_{i = 1}p_i^{x_i}, 0 \leq x_i \leq m, \sum^{k}_{i = 1}x_i = m$

## class multinomial¶

Syntax

namespace oneapi::mkl::rng {
template<typename IntType = std::int32_t, typename Method = multinomial_method::by_default>
class multinomial {
public:
using method_type = Method;
using result_type = IntType;
explicit multinomial(double ntrial, std::vector<double> p);
std::int32_t ntrial() const;
std::vector<double> p() const;
};
}


Template parameters

typename IntType
Type of the produced values. Supported types:
• std::int32_t

• std::uint32_t

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

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

• oneapi::mkl::rng::multinomial_method::by_default

• oneapi::mkl::rng::multinomial_method::poisson_icdf_based

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

explicit multinomial(double ntrial, std::vector<double> p)

Constructor with parameters

std::int32_t ntrial() const

Method to obtain number of independent trials

std::vector<double> p() const

Method to obtain probability vector of possible outcomes

Member types

multinomial::method_type = Method


Description

The type which defines the transformation method for generation.

multinomial::result_type = IntType


Description

The type which defines the type of generated random numbers.

Constructors

explicit multinomial::multinomial(double ntrial, std::vector<double> p)


Description

Constructor with parameters. ntrial is a number of independent trials, p is a probability vector.

Throws

oneapi::mkl::invalid_argument

Exception is thrown when $$ntrial < 0$$, or $$p.size() < 1$$

Characteristics

std::int32_t multinomial::ntrial() const


Return Value

Returns the distribution parameter ntrial.

std::vector<double> multinomial::p() const


Return Value

Returns the distribution parameter p.

Parent topic: Distributions