29 Numerics library [numerics]

A normal_­distribution random number distribution produces random numbers x distributed according to the probability density function

$$p(x|\mu ,\sigma )=\frac{1}{\sigma \sqrt{2\pi }}\cdot \exp \left(-\frac{(x-\mu {)}^2}{2{\sigma }^2}\right)\text{.}$$

The distribution parameters μ and σ are also known as this distribution's mean and standard deviation.

template<class RealType = double>
  class normal_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructors and reset functions
    explicit normal_distribution(RealType mean = 0.0, RealType stddev = 1.0);
    explicit normal_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
    RealType mean() const;
    RealType stddev() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A lognormal_­distribution random number distribution produces random numbers $x>0$ distributed according to the probability density function

$$p(x|m,s)=\frac{1}{sx\sqrt{2\pi }}\cdot \exp \left(-\frac{(\ln x-m{)}^2}{2s^2}\right)\text{.}$$

template<class RealType = double>
  class lognormal_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    explicit lognormal_distribution(RealType m = 0.0, RealType s = 1.0);
    explicit lognormal_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
    RealType m() const;
    RealType s() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A chi_­squared_­distribution random number distribution produces random numbers x>0 distributed according to the probability density function

$$p\left(x|n\right)=\frac{x^{\left(n/2\right)-1}\cdot e^{-x/2}}{\Gamma \left(n/2\right)\cdot 2^{n/2}}\text{.}$$

template<class RealType = double>
  class chi_squared_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    explicit chi_squared_distribution(RealType n = 1);
    explicit chi_squared_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
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A cauchy_­distribution random number distribution produces random numbers x distributed according to the probability density function

$$p(x|a,b)={\left(\pi b\left(1+{\left(\frac{x-a}{b}\right)}^2\right)\right)}^{-1}\text{.}$$

template<class RealType = double>
  class cauchy_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    explicit cauchy_distribution(RealType a = 0.0, RealType b = 1.0);
    explicit cauchy_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
    RealType a() const;
    RealType b() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A fisher_­f_­distribution random number distribution produces random numbers x≥0 distributed according to the probability density function

$$p(x|m,n)=\frac{\Gamma ((m+n)/2)}{\Gamma \left(m/2\right)\Gamma \left(n/2\right)}\cdot {\left(\frac{m}{n}\right)}^{m/2}\cdot x^{\left(m/2\right)-1}\cdot {\left(1+\frac{mx}{n}\right)}^{-(m+n)/2}\text{.}$$

template<class RealType = double>
  class fisher_f_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    explicit fisher_f_distribution(RealType m = 1, RealType n = 1);
    explicit fisher_f_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
    RealType m() const;
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A student_­t_­distribution random number distribution produces random numbers x distributed according to the probability density function

$$p\left(x|n\right)=\frac{1}{\sqrt{n\pi }}\cdot \frac{\Gamma ((n+1)/2)}{\Gamma \left(n/2\right)}\cdot {\left(1+\frac{x^2}{n}\right)}^{-(n+1)/2}\text{.}$$

template<class RealType = double>
  class student_t_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    explicit student_t_distribution(RealType n = 1);
    explicit student_t_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
    RealType n() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };