29 Numerics library [numerics]

29.5 Random number generation [rand]

29.5.9 Random number distribution class templates [rand.dist]

29.5.9.3 Bernoulli distributions [rand.dist.bern]

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

A bernoulli_distribution random number distribution produces bool values b distributed according to the discrete probability function in Formula 29.4 .

\begin{matrix} P (b | p) = {\begin{matrix} p & if b = true 1 - p & if b = false \end{matrix} \\ (29.4) \end{matrix}

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namespace std { 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(); // equality operators friend bool operator==(const bernoulli_distribution& x, const bernoulli_distribution& y); // 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; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const bernoulli_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, bernoulli_distribution& x); }; }

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explicit bernoulli_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.

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

A binomial_distribution random number distribution produces integer values i ≥ 0 distributed according to the discrete probability function in Formula 29.5 .

\begin{matrix} P (i | t, p) = (\frac{t}{i}) \cdot p^{i} \cdot (1 - p)^{t - i} \\ (29.5) \end{matrix}

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namespace std { 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(); // equality operators friend bool operator==(const binomial_distribution& x, const binomial_distribution& y); // 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; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const binomial_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, binomial_distribution& x); }; }

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

Preconditions: 0 ≤ p ≤ 1 and 0 ≤ 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.

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

A geometric_distribution random number distribution produces integer values i ≥ 0 distributed according to the discrete probability function in Formula 29.6 .

\begin{matrix} P (i | p) = p \cdot (1 - p)^{i} \\ (29.6) \end{matrix}

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namespace std { 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(); // equality operators friend bool operator==(const geometric_distribution& x, const geometric_distribution& y); // 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; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const geometric_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, geometric_distribution& x); }; }

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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.

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

A negative_binomial_distribution random number distribution produces random integers i ≥ 0 distributed according to the discrete probability function in Formula 29.7 .

\begin{matrix} P (i | k, p) = (\frac{k + i - 1}{i}) \cdot p^{k} \cdot (1 - p)^{i} \\ (29.7) \end{matrix}

[Note 1:

This implies that P(i | k,p) is undefined when p == 1.

— end note]

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namespace std { 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(); // equality operators friend bool operator==(const negative_binomial_distribution& x, const negative_binomial_distribution& y); // 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; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const negative_binomial_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, negative_binomial_distribution& x); }; }

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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.