# binomial¶

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

Description

The class object is used in the oneapi::mkl::rng::generate() function to provide random numbers binomially distributed with a number of independent Bernoulli trials $$m$$, and with probability $$p$$ of a single trial success, where $$p \in R; 0 \leq p \leq 1, m \in N$$.

A binomially distributed variate represents the number of successes in $$m$$ independent Bernoulli trials with probability of a single trial success $$p$$.

The probability distribution is given by:

$P(X = k) = C^k_{m}p^k(1 - p)^{m - k}, k \in \{0, 1, ... , m\}$

The cumulative distribution function is as follows:

$\begin{split}F_{m, p}(x) = \left\{ \begin{array}{rcl} 0, x < 0 \\ \sum^{\lfloor x \rfloor}_{k = 0} C^k_{m}p^k(1 - p)^{m - k}, 0 \leq x < m, x \in R \\ 1, x \ge m \end{array}\right.\end{split}$

## class binomial¶

Syntax

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


Template parameters

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

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

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

• oneapi::mkl::rng::binomial_method::by_default

• oneapi::mkl::rng::binomial_method::btpe

See description of the methods in Distributions methods template parameter.

Class Members

Routine

Description

binomial()

Default constructor

explicit binomial(std::int32_t ntrial, double p)

Constructor with parameters

std::int32_t ntrial() const

Method to obtain number of independent trials m

double p() const

Method to obtain success probability of a single trial p

Member types

binomial::method_type = Method


Description

The type which defines transformation method for generation.

binomial::result_type = IntType


Description

The type which defines type of generated random numbers.

Constructors

binomial::binomial()


Description

Default constructor for distribution, parameters set as m = 5, p = 0.5.

explicit binomial::binomial(std::int32_t ntrial, double p)


Description

Constructor with parameters. ntrial is the number of independent trials, p is the success probability of a single trial.

Throws

oneapi::mkl::invalid_argument

Exception is thrown when $$p > 1.0$$, or $$p < 0.0$$, or $$ntrial < 1$$

Characteristics

std::int32_t binomial::ntrial() const


Return Value

Returns the distribution parameter m - number of independent trials.

double binomial::p() const


Return Value

Returns the distribution parameter p - success probability of a single trial.

Parent topic: Distributions