29 Numerics library [numerics]

A poisson_­distribution random number distribution produces integer values $i\ge 0$ distributed according to the discrete probability function

$$P\left(i|\mu \right)=\frac{e^{-\mu }{\mu }^i}{i!}\text{.}$$

The distribution parameter μ is also known as this distribution's mean.

template<class IntType = int>
  class poisson_distribution
  {
  public:
    // types
    using result_type = IntType;
    using param_type  = unspecified;

    // constructors and reset functions
    explicit poisson_distribution(double mean = 1.0);
    explicit poisson_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 mean() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

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

$$p\left(x|\lambda \right)=\lambda e^{-\lambda x}\text{.}$$

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

    // constructors and reset functions
    explicit exponential_distribution(RealType lambda = 1.0);
    explicit exponential_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 lambda() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

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

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

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

    // constructors and reset functions
    explicit gamma_distribution(RealType alpha = 1.0, RealType beta = 1.0);
    explicit gamma_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 alpha() const;
    RealType beta() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

A weibull_­distribution random number distribution produces random numbers $x\ge 0$ distributed according to the probability density function

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

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

    // constructor and reset functions
    explicit weibull_distribution(RealType a = 1.0, RealType b = 1.0);
    explicit weibull_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;
  };

An extreme_­value_­distribution random number distribution produces random numbers x distributed according to the probability density function274

$$p(x|a,b)=\frac{1}{b}\cdot \exp \left(\frac{a-x}{b}-\exp \left(\frac{a-x}{b}\right)\right)\text{.}$$

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

    // constructor and reset functions
    explicit extreme_value_distribution(RealType a = 0.0, RealType b = 1.0);
    explicit extreme_value_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;
  };