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 $p_i\in R;0\le p_i\le 1;m,k\in N$.

The probability distribution is given by:

$$P(X_1=x_1,...,X_k=x_k)=\frac{m!}{{\mathrm{\Pi }}_{i=1}^k{x}_i!}{\mathrm{\Pi }}_{i=1}^k{p}_i^{x_i},0\le x_i\le m,\sum _{i=1}^k{x}_i=m$$

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