26 Numerics library [numerics]

26.6 Random number generation [rand]

26.6.8 Random number distribution class templates [rand.dist]

26.6.8.3 Bernoulli distributions [rand.dist.bern]

26.6.8.3.1 Class bernoulli_distribution [rand.dist.bern.bernoulli]

1

A bernoulli_distribution random number distribution produces bool values b distributed according to the discrete probability function \[% P(b\,|\,p) = \left\{ \begin{array}{lcl} p & \mbox{if} & b = \texttt{true} \\ 1-p & \mbox{if} & b = \texttt{false} \end{array}\right. \; \mbox{.} \]

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

 // constructors and reset functions
 explicit bernoulli_distribution(double p = 0.5);
 explicit bernoulli_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 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);

2

Requires: 0 ≤ p ≤ 1.

3

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

double p() const;

4

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

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

1

A binomial_distribution random number distribution produces integer values i ≥ 0 distributed according to the discrete probability function\[% P(i\,|\,t,p) = \binom{t}{i} \cdot p^i \cdot (1-p)^{t-i} \; \mbox{.} \]

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

 // constructors and reset functions
 explicit binomial_distribution(IntType t = 1, double p = 0.5);
 explicit binomial_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
 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);

2

Requires: 0 ≤ p ≤ 1 and 0 ≤ t .

3

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

IntType t() const;

4

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

double p() const;

5

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

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

1

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:
 // types
 using result_type = IntType;
 using param_type  = unspecified;

 // constructors and reset functions
 explicit geometric_distribution(double p = 0.5);
 explicit geometric_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 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);

2

Requires: 0 < p < 1.

3

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

double p() const;

4

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

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

1

A negative_binomial_distribution random number distribution produces random integers i ≥ 0 distributed according to the discrete probability function \[% P(i\,|\,k,p) = \binom{k+i-1}{i} \cdot p^k \cdot (1-p)^i \; \mbox{.} \] [ Note: This implies that P(i | k,p) is undefined when p == 1.  — end note ]

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

 // constructor and reset functions
 explicit negative_binomial_distribution(IntType k = 1, double p = 0.5);
 explicit negative_binomial_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
 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);

2

Requires: 0 < p ≤ 1 and 0 < k .

3

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

IntType k() const;

4

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

double p() const;

5

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