28 Numerics library [numerics]

28.5 Random number generation [rand]

28.5.9 Random number distribution class templates [rand.dist]

28.5.9.4 Poisson distributions [rand.dist.pois]

28.5.9.4.1 Class template poisson_distribution [rand.dist.pois.poisson]

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A poisson_distribution random number distribution produces integer values i  ≥ 0 distributed according to the discrete probability function
The distribution parameter μ is also known as this distribution's mean.
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template<class IntType = int> class poisson_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructors and reset functions poisson_distribution() : poisson_distribution(1.0) {} explicit poisson_distribution(double mean); explicit poisson_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const poisson_distribution& x, const poisson_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 mean() 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 poisson_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, poisson_distribution& x); };
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explicit poisson_distribution(double mean);
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Preconditions: .
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Remarks: mean corresponds to the parameter of the distribution.
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double mean() const;
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Returns: The value of the mean parameter with which the object was constructed.

28.5.9.4.2 Class template exponential_distribution [rand.dist.pois.exp]

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An exponential_distribution random number distribution produces random numbers distributed according to the probability density function
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namespace std { template<class RealType = double> class exponential_distribution { public: // types using result_type = RealType; using param_type = unspecified; // constructors and reset functions exponential_distribution() : exponential_distribution(1.0) {} explicit exponential_distribution(RealType lambda); explicit exponential_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const exponential_distribution& x, const exponential_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 RealType lambda() 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 exponential_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, exponential_distribution& x); }; }
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explicit exponential_distribution(RealType lambda);
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Preconditions: .
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Remarks: lambda corresponds to the parameter of the distribution.
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RealType lambda() const;
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Returns: The value of the lambda parameter with which the object was constructed.

28.5.9.4.3 Class template gamma_distribution [rand.dist.pois.gamma]

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A gamma_distribution random number distribution produces random numbers distributed according to the probability density function
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namespace std { template<class RealType = double> class gamma_distribution { public: // types using result_type = RealType; using param_type = unspecified; // constructors and reset functions gamma_distribution() : gamma_distribution(1.0) {} explicit gamma_distribution(RealType alpha, RealType beta = 1.0); explicit gamma_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const gamma_distribution& x, const gamma_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 RealType alpha() const; RealType beta() 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 gamma_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, gamma_distribution& x); }; }
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explicit gamma_distribution(RealType alpha, RealType beta = 1.0);
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Preconditions: and .
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Remarks: alpha and beta correspond to the parameters of the distribution.
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RealType alpha() const;
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Returns: The value of the alpha parameter with which the object was constructed.
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RealType beta() const;
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Returns: The value of the beta parameter with which the object was constructed.

28.5.9.4.4 Class template weibull_distribution [rand.dist.pois.weibull]

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A weibull_distribution random number distribution produces random numbers x  ≥ 0 distributed according to the probability density function
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namespace std { template<class RealType = double> class weibull_distribution { public: // types using result_type = RealType; using param_type = unspecified; // constructor and reset functions weibull_distribution() : weibull_distribution(1.0) {} explicit weibull_distribution(RealType a, RealType b = 1.0); explicit weibull_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const weibull_distribution& x, const weibull_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 RealType a() const; RealType b() 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 weibull_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, weibull_distribution& x); }; }
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explicit weibull_distribution(RealType a, RealType b = 1.0);
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Preconditions: and .
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Remarks: a and b correspond to the respective parameters of the distribution.
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RealType a() const;
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Returns: The value of the a parameter with which the object was constructed.
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RealType b() const;
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Returns: The value of the b parameter with which the object was constructed.

28.5.9.4.5 Class template extreme_value_distribution [rand.dist.pois.extreme]

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An extreme_value_distribution random number distribution produces random numbers x distributed according to the probability density function231
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namespace std { template<class RealType = double> class extreme_value_distribution { public: // types using result_type = RealType; using param_type = unspecified; // constructor and reset functions extreme_value_distribution() : extreme_value_distribution(0.0) {} explicit extreme_value_distribution(RealType a, RealType b = 1.0); explicit extreme_value_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const extreme_value_distribution& x, const extreme_value_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 RealType a() const; RealType b() 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 extreme_value_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, extreme_value_distribution& x); }; }
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explicit extreme_value_distribution(RealType a, RealType b = 1.0);
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Preconditions: .
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Remarks: a and b correspond to the respective parameters of the distribution.
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RealType a() const;
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Returns: The value of the a parameter with which the object was constructed.
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RealType b() const;
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Returns: The value of the b parameter with which the object was constructed.
231)231)
The distribution corresponding to this probability density function is also known (with a possible change of variable) as the Gumbel Type I, the log-Weibull, or the Fisher-Tippett Type I distribution.