26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.8 Random number distribution class templates [rand.dist]

26.6.8.4 Poisson distributions [rand.dist.pois]

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

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A poisson_­distribution random number distribution produces integer values distributed according to the discrete probability function
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
    poisson_distribution() : poisson_distribution(1.0) {}
    explicit poisson_distribution(double mean);
    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;
  };
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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.

26.6.8.4.2 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
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();

    // 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;
  };
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explicit exponential_distribution(RealType lambda);
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Preconditions: .
3
#
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.

26.6.8.4.3 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
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();

    // 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;
  };
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explicit gamma_distribution(RealType alpha, RealType beta = 1.0);
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Preconditions: and .
3
#
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.

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

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A weibull_­distribution random number distribution produces random numbers distributed according to the probability density function
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();

    // 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 weibull_distribution(RealType a, RealType b = 1.0);
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Preconditions: and .
3
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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.

26.6.8.4.5 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 function247 
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();

    // 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 extreme_value_distribution(RealType a, RealType b = 1.0);
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Preconditions: .
3
#
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.
247)
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.
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