26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.8 Random number distribution class templates [rand.dist]

26.6.8.5 Normal distributions [rand.dist.norm]

26.6.8.5.1 Class template normal_­distribution [rand.dist.norm.normal]

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A normal_­distribution random number distribution produces random numbers x distributed according to the probability density function
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
    normal_distribution() : normal_distribution(0.0) {}
    explicit normal_distribution(RealType mean, 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;
  };
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explicit normal_distribution(RealType mean, RealType stddev = 1.0);
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Preconditions: .
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Remarks: mean and stddev correspond to the respective parameters of the distribution.
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RealType mean() const;
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Returns: The value of the mean parameter with which the object was constructed.
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RealType stddev() const;
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Returns: The value of the stddev parameter with which the object was constructed.

26.6.8.5.2 Class template lognormal_­distribution [rand.dist.norm.lognormal]

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A lognormal_­distribution random number distribution produces random numbers distributed according to the probability density function
template<class RealType = double>
  class lognormal_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    lognormal_distribution() : lognormal_distribution(0.0) {}
    explicit lognormal_distribution(RealType m, 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;
  };
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explicit lognormal_distribution(RealType m, RealType s = 1.0);
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Preconditions: .
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Remarks: m and s correspond to the respective parameters of the distribution.
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RealType m() const;
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Returns: The value of the m parameter with which the object was constructed.
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RealType s() const;
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Returns: The value of the s parameter with which the object was constructed.

26.6.8.5.3 Class template chi_­squared_­distribution [rand.dist.norm.chisq]

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A chi_­squared_­distribution random number distribution produces random numbers distributed according to the probability density function
template<class RealType = double>
  class chi_squared_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    chi_squared_distribution() : chi_squared_distribution(1.0) {}
    explicit chi_squared_distribution(RealType n);
    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;
  };
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explicit chi_squared_distribution(RealType n);
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Preconditions: .
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Remarks: n corresponds to the parameter of the distribution.
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RealType n() const;
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Returns: The value of the n parameter with which the object was constructed.

26.6.8.5.4 Class template cauchy_­distribution [rand.dist.norm.cauchy]

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A cauchy_­distribution random number distribution produces random numbers x distributed according to the probability density function
template<class RealType = double>
  class cauchy_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    cauchy_distribution() : cauchy_distribution(0.0) {}
    explicit cauchy_distribution(RealType a, 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;
  };
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explicit cauchy_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.

26.6.8.5.5 Class template fisher_­f_­distribution [rand.dist.norm.f]

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A fisher_­f_­distribution random number distribution produces random numbers distributed according to the probability density function
template<class RealType = double>
  class fisher_f_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    fisher_f_distribution() : fisher_f_distribution(1.0) {}
    explicit fisher_f_distribution(RealType m, RealType n = 1.0);
    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;
  };
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explicit fisher_f_distribution(RealType m, RealType n = 1);
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Preconditions: and .
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Remarks: m and n correspond to the respective parameters of the distribution.
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RealType m() const;
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Returns: The value of the m parameter with which the object was constructed.
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RealType n() const;
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Returns: The value of the n parameter with which the object was constructed.

26.6.8.5.6 Class template student_­t_­distribution [rand.dist.norm.t]

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A student_­t_­distribution random number distribution produces random numbers x distributed according to the probability density function
template<class RealType = double>
  class student_t_distribution {
  public:
    // types
    using result_type = RealType;
    using param_type  = unspecified;

    // constructor and reset functions
    student_t_distribution() : student_t_distribution(1.0) {}
    explicit student_t_distribution(RealType n);
    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;
  };
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explicit student_t_distribution(RealType n);
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Preconditions: .
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Remarks: n corresponds to the parameter of the distribution.
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RealType n() const;
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Returns: The value of the n parameter with which the object was constructed.