cppdraft_translate/cppdraft/rand/dist/bern.md

[rand.dist.bern]

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]

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

P(b|p)={p if b=true1−p if b=false(29.4)

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namespace std {class bernoulli_distribution {public:// typesusing 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 operatorsfriend bool operator==(const bernoulli_distribution& x, const bernoulli_distribution& y); // generating functionstemplate result_type operator()(URBG& g); template result_type operator()(URBG& g, const param_type& parm); // property functionsdouble p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractorstemplate<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);

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Preconditions: 0 ≤ p ≤ 1.

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Remarks: p corresponds to the parameter of the distribution.

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double p() const;

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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]

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

P(i|t,p)=(ti)â‹piâ‹(1−p)t−i(29.5)

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namespace std {templateclass binomial_distribution {public:// typesusing 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 operatorsfriend bool operator==(const binomial_distribution& x, const binomial_distribution& y); // generating functionstemplate result_type operator()(URBG& g); template 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 extractorstemplate<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);

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Preconditions: 0 ≤ p ≤ 1 and 0 ≤ t.

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

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IntType t() const;

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

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double p() const;

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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]

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

P(i|p)=pâ‹(1−p)i(29.6)

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namespace std {templateclass geometric_distribution {public:// typesusing 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 operatorsfriend bool operator==(const geometric_distribution& x, const geometric_distribution& y); // generating functionstemplate result_type operator()(URBG& g); template result_type operator()(URBG& g, const param_type& parm); // property functionsdouble p() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractorstemplate<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);

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Preconditions: 0<p<1.

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Remarks: p corresponds to the parameter of the distribution.

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double p() const;

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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]

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

P(i|k,p)=(k+i−1i)â‹pkâ‹(1−p)i(29.7)

[Note 1:

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

— end note]

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namespace std {templateclass negative_binomial_distribution {public:// typesusing 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 operatorsfriend bool operator==(const negative_binomial_distribution& x, const negative_binomial_distribution& y); // generating functionstemplate result_type operator()(URBG& g); template 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 extractorstemplate<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);

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Preconditions: 0<p≤1 and 0<k.

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

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IntType k() const;

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

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double p() const;

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