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

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:

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

The cumulative distribution function is as follows:

$$\begin{array}{r}{F}_{m,p}(x)=\{\begin{array}{r}0,x<0\\ \sum _{k=0}^{\lfloor x\rfloor }{C}_m^k{p}^k(1-p{)}^{m-k},0\le x<m,x\in R\\ 1,x\ge m\end{array}\end{array}$$

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

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