26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.9 Random number distribution class templates [rand.dist]

26.6.9.3 Bernoulli distributions [rand.dist.bern]

26.6.9.3.1 Class bernoulli_distribution [rand.dist.bern.bernoulli]

A bernoulli_distribution random number distribution produces bool values b distributed according to the discrete probability function

P (b | p) = {\begin{matrix} p & if b = true, or 1 - p & if b = false . \end{matrix}

class bernoulli_distribution { public: // types using result_type = bool; using param_type = unspecified; // constructors and reset functions bernoulli_distribution() : bernoulli_distribution(0.5) {} explicit bernoulli_distribution(double p); explicit bernoulli_distribution(const param_type& parm); void reset(); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; };

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explicit bernoulli_distribution(double p);

Preconditions:

0 \leq p \leq 1

Remarks: p corresponds to the parameter of the distribution.

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double p() const;

Returns: The value of the p parameter with which the object was constructed.

26.6.9.3.2 Class template binomial_distribution [rand.dist.bern.bin]

A binomial_distribution random number distribution produces integer values

i \geq 0

distributed according to the discrete probability function

P (i | t, p) = (\frac{t}{i}) \cdot p^{i} \cdot (1 - p)^{t - i} .

template<class IntType = int> class binomial_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructors and reset functions binomial_distribution() : binomial_distribution(1) {} explicit binomial_distribution(IntType t, double p = 0.5); explicit binomial_distribution(const param_type& parm); void reset(); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions IntType t() const; double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; };

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explicit binomial_distribution(IntType t, double p = 0.5);

Preconditions:

0 \leq p \leq 1

and

0 \leq t

Remarks: t and p correspond to the respective parameters of the distribution.

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IntType t() const;

Returns: The value of the t parameter with which the object was constructed.

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double p() const;

Returns: The value of the p parameter with which the object was constructed.

26.6.9.3.3 Class template geometric_distribution [rand.dist.bern.geo]

A geometric_distribution random number distribution produces integer values

i \geq 0

distributed according to the discrete probability function

P (i | p) = p \cdot (1 - p)^{i} .

template<class IntType = int> class geometric_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructors and reset functions geometric_distribution() : geometric_distribution(0.5) {} explicit geometric_distribution(double p); explicit geometric_distribution(const param_type& parm); void reset(); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; };

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explicit geometric_distribution(double p);

Preconditions:

0 < p < 1

Remarks: p corresponds to the parameter of the distribution.

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double p() const;

Returns: The value of the p parameter with which the object was constructed.

26.6.9.3.4 Class template negative_binomial_distribution [rand.dist.bern.negbin]

A negative_binomial_distribution random number distribution produces random integers

i \geq 0

distributed according to the discrete probability function

P (i | k, p) = (\frac{k + i - 1}{i}) \cdot p^{k} \cdot (1 - p)^{i} .

[Note 1:

This implies that

P (i | k, p)

is undefined when p == 1.

— end note]

template<class IntType = int> class negative_binomial_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructor and reset functions negative_binomial_distribution() : negative_binomial_distribution(1) {} explicit negative_binomial_distribution(IntType k, double p = 0.5); explicit negative_binomial_distribution(const param_type& parm); void reset(); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions IntType k() const; double p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; };

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explicit negative_binomial_distribution(IntType k, double p = 0.5);

Preconditions:

0 < p \leq 1

and

0 < k

Remarks: k and p correspond to the respective parameters of the distribution.

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IntType k() const;

Returns: The value of the k parameter with which the object was constructed.

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double p() const;

Returns: The value of the p parameter with which the object was constructed.

26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.9 Random number distribution class templates [rand.dist]

26.6.9.3 Bernoulli distributions [rand.dist.bern]

26.6.9.3.1 Class bernoulli_­distribution [rand.dist.bern.bernoulli]

26.6.9.3.2 Class template binomial_­distribution [rand.dist.bern.bin]

26.6.9.3.3 Class template geometric_­distribution [rand.dist.bern.geo]

26.6.9.3.4 Class template negative_­binomial_­distribution [rand.dist.bern.negbin]

26.6.9.3.1 Class bernoulli_distribution [rand.dist.bern.bernoulli]

26.6.9.3.2 Class template binomial_distribution [rand.dist.bern.bin]

26.6.9.3.3 Class template geometric_distribution [rand.dist.bern.geo]

26.6.9.3.4 Class template negative_binomial_distribution [rand.dist.bern.negbin]