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Showing content from https://timsong-cpp.github.io/cppwp/n4659/rand.dist.bern below:

[rand.dist.bern]

29 Numerics library [numerics] 29.6 Random number generation [rand] 29.6.8 Random number distribution class templates [rand.dist] 29.6.8.3 Bernoulli distributions [rand.dist.bern] 29.6.8.3.1 Class bernoulli_distribution [rand.dist.bern.bernoulli]

A bernoulli_distribution random number distribution produces bool values b distributed according to the discrete probability function

P(b|p)={pifb=true1−pifb=false.

class bernoulli_distribution {
public:
    using result_type = bool;
  using param_type  = unspecified;

    explicit bernoulli_distribution(double p = 0.5);
  explicit bernoulli_distribution(const param_type& parm);
  void reset();

    template<class URBG>
    result_type operator()(URBG& g);
  template<class URBG>
    result_type operator()(URBG& g, const param_type& parm);

    double p() const;
  param_type param() const;
  void param(const param_type& parm);
  result_type min() const;
  result_type max() const;
};

explicit bernoulli_distribution(double p = 0.5);

Effects: Constructs a bernoulli_distribution object; p corresponds to the parameter of the distribution.

double p() const;

Returns: The value of the p parameter with which the object was constructed.

29.6.8.3.2 Class template binomial_distribution [rand.dist.bern.bin]

A binomial_distribution random number distribution produces integer values i≥0 distributed according to the discrete probability function

P(i|t,p)=(ti)⋅pi⋅(1−p)t−i.

template<class IntType = int>
  class binomial_distribution {
  public:
        using result_type = IntType;
    using param_type  = unspecified;

        explicit binomial_distribution(IntType t = 1, double p = 0.5);
    explicit binomial_distribution(const param_type& parm);
    void reset();

        template<class URBG>
      result_type operator()(URBG& g);
    template<class URBG>
      result_type operator()(URBG& g, const param_type& parm);

        IntType t() const;
    double p() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

explicit binomial_distribution(IntType t = 1, double p = 0.5);

Effects: Constructs a binomial_distribution object; t and p correspond to the respective parameters of the distribution.

IntType t() const;

Returns: The value of the t parameter with which the object was constructed.

double p() const;

Returns: The value of the p parameter with which the object was constructed.

29.6.8.3.3 Class template geometric_distribution [rand.dist.bern.geo]

A geometric_distribution random number distribution produces integer values i≥0 distributed according to the discrete probability function

P(i|p)=p⋅(1−p)i.

template<class IntType = int>
  class geometric_distribution {
  public:
        using result_type = IntType;
    using param_type  = unspecified;

        explicit geometric_distribution(double p = 0.5);
    explicit geometric_distribution(const param_type& parm);
    void reset();

        template<class URBG>
      result_type operator()(URBG& g);
    template<class URBG>
      result_type operator()(URBG& g, const param_type& parm);

        double p() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

explicit geometric_distribution(double p = 0.5);

Effects: Constructs a geometric_distribution object; p corresponds to the parameter of the distribution.

double p() const;

Returns: The value of the p parameter with which the object was constructed.

29.6.8.3.4 Class template negative_binomial_distribution [rand.dist.bern.negbin]

A negative_binomial_distribution random number distribution produces random integers i≥0 distributed according to the discrete probability function

P(i|k,p)=(k+i−1i)⋅pk⋅(1−p)i.

[ Note: This implies that P(i|k,p) is undefined when p == 1. — end note ]

template<class IntType = int>
  class negative_binomial_distribution {
  public:
        using result_type = IntType;
    using param_type  = unspecified;

        explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);
    explicit negative_binomial_distribution(const param_type& parm);
    void reset();

        template<class URBG>
      result_type operator()(URBG& g);
    template<class URBG>
      result_type operator()(URBG& g, const param_type& parm);

        IntType k() const;
    double p() const;
    param_type param() const;
    void param(const param_type& parm);
    result_type min() const;
    result_type max() const;
  };

explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);

Effects: Constructs a negative_binomial_distribution object; k and p correspond to the respective parameters of the distribution.

IntType k() const;

Returns: The value of the k parameter with which the object was constructed.

double p() const;

Returns: The value of the p parameter with which the object was constructed.

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